This company is lowballing you taking undue advantage of your situation. You should rather wait till you get a job which acknowledges your complete experience.
There are multiple other ways to document your work experience in the absence of a relieving letter:
Salary Slips: Salary slip is a proof of employment, essentially by definition if you think about it. As you would readily agree, if you don't have them, you are unlikely to get them now, since you left the company on less than ideal terms.
Salary Account Statement: In all reputed Indian IT companies, salary is paid via fund transfer to the employee's salary account. In the absence of salary slips, bank statements should serve the purpose well. Of course, this only works if the credit entry is explicitly described as a "Salary Credit" by "Company ABC", not a generic NEFT transaction.
Banks in India have been providing the option of e-Statements for about a decade now. If you happen to have registered for e-Statements back then, search through your old emails and keep these statements handy. It would certainly help with future job applications, if not right away. If you don't have those e-Statements, then get ready to follow the painful procedure of requesting the bank to issue duplicate statements from years ago.
Form 16: This form declares the tax deducted at source (TDS) by the employer. It serves as an indirect employment proof, because it is given only to salaried employees. It is also an inaccurate one, because the form typically lists one TDS entry per quarter which does not make it clear if you were employed for the entire quarter.
Annual Salary Hike Letter: The letter proves that you were employed with the company on the date mentioned in the letter. If you left the company just after receiving the appraisal letter, then you are in luck. If you left several months later, it is of lesser value. Of course, if you don't have this letter, then forget about it.
Legal declaration: When all else fails, the employee can submit a signed legal declaration to the employer. Employers in India regularly accept such declarations for various purposes (not necessarily cases involving lack of relieving letter) where obtaining a "proper" proof is cumbersome and/or not of critical importance.
A company has a mechanism to deal with the non-standard or exceptional cases, in addition to the standard set of processes. Well-established companies will usually have a established procedure to deal with exceptional cases. Less established ones may take a
Calvinball "make up rules as you go" approach, which often means "when we have a situation we don't know how to handle, do as so-and-so says".
A candidate showing up without a relieving letter is a common scenario, and I would have expected the HR to tell you the alternatives. If the company were really excited about hiring you, they would have figured out a means to give you a fair deal. That they chose to try to take advantage of your situation strikes me as a huge red flag.
The company's claim that "lack of a relieving letter will cause problems in background verification" is, to put it mildly, nonsense. The company decides what to do with the background verification data. You have already explained to them your "missing" experience, so there is no reason why the background verification should cause them any surprise, let alone "problems". In other words, they are trying to trick you into accepting a less senior role at a lower salary.
You have already acknowledged your mistake of not leaving the company on good terms, so I won't lecture you on that. :-) However, the company doesn't get the license to take advantage of your mistake.
Your instinct is correct, omitting experience would also be a mistake, as it would put you at a disadvantage during future job searches. Job listings in India (and also in other countries) typically ask for "minimum years of experience" as a shortlisting criteria, especially for senior level roles.
If this company doesn't acknowledge your complete experience, you should rather wait until you find someone that does. In addition, it would be prudent to request the new company to give you a letter stating the number of years of experience they considered while hiring you soon after you join. HR typically doesn't have a problem handing this letter, my current company and the previous one even mention it in the appointment letter. This gives you an easy chance to "fix" your work experience for good.
Now coming to your questions on NASSCOM:
- NASSCOM maintains the National Skills Registry, which doesn't have any provision for "blacklisting".
- Only a limited number of Indian companies are registered with NSR. These are mainly companies that are predominantly service-oriented and/or serve mostly foreign clients. Even if you are "blacklisted" (whatever that is taken to mean), there is still a huge market open for you.
The NSR background verification process is described on their website. The information on this page and this page is relevant to your question:
Background check may be requested by the present employer company or by a NSR Subscriber company authorised by the registered professional or by the professional himself / herself. If a company has requested background check, the terms and conditions of background check, reporting requirements etc. are determined mutually by such company and EBC selected by it. In addition to reporting the results to the company, the EBC will also record the results of background verification on NSR against the details of the professional.
In order to keep their NSR profile ready with background check results, the professional can also request for a background check on details recorded by them on NSR. Verification request can be for personal details like date of birth, father's name, passport number, Permanent Account Number (PAN) or for present and permanent address, academic qualification, technical qualification and employment details.
If EBC's remarks are not factually correct, how can I get it corrected?
If the remarks inserted by EBC are not factually correct, you may approach EBC with clarifications / additional documentation etc. If the circumstances so require, EBC will re-verify its report and get the report corrected.
If you are concerned about the NSR background verification, you could initiate the background verification yourself and try to get the "missing" experience corrected by providing the EBC with suitable explanation or documents or whatever else they need. When the company initiates it, you have lesser control over the process.