Hi I was offered a 1 year maternity leave position and I signed the offer letter. The letter is called "Term Agreement Letter" and it states the start and and end dates. However they said that the offer is conditional based on a successfully completed background check by the starting date. I signed all the forms to release the info for my background check and now I am waiting. However I have received phone calls from other companies for interviews, and a couple of them are permanent full time and I like them. What if I receive an offer and still I am waiting for my background check with the other company? Can I withdraw my acceptance after I signed the Offer Letter?
100% continue to interview for the positions you want and continue with onboarding with this company. This never stops being true.
A company would not hesitate to replace you with someone who was "perfect" or if you weren't what they wanted. Maybe this turns in to a full time role, but as it stands, it's just a mat leave stand in. In the end, outside of legal obligations that you might have (and that requires legal advice), you owe a company nothing.
Now, that being said, it doesn't mean there won't be hurt feelings. The situation is the same as when a boss who likes you is telling you that you're getting laid off. It's nothing personal, it's "just business".
Can I withdraw my acceptance after I signed the Offer Letter?
There may be consequences of doing so. For example people in the company you've signed offer letter with are very unlikely to consider you for hiring in the future (including in future companies where they may be employed). In some extreme circumstances it could end in litigation, though that's mostly an academic possibility unless you've accepted some sort of a sign-on bonus.
Though I have to say that unless the agents came over with firm offers in hand I would not go burning a sure thing just yet, as you may wind up with no job and a recently burned bridge so make sure that you have everything aligned with another company first (or that you can take the possible unemployment).
If you decide to withdraw the letter, there are some mitigation strategies.
If stuck in the limbo of waiting for another offer you can stall the background check as this usually will require for you to fork over some documents which may take you some time to locate. While I personally would not choose this method as it's pretty sleazy, it is an option for sure.
Alternatively, and my perferred option, is to be honest with the company and tell them that you want some extra time to consider the offer. Do not give them a specific reason like "i got a better interview lined up" (even though it's obvious) as that will not help you, and then they can either say no - in which case you are where you wanted to be, or they can agree in which case you just bought more time to get a better offer somewhere else.
Imo either way you are better of than just outright going back on the offer.
The situation is extremely simple,
They have offered you nothing.
This is another case of incredible abuse of employees, in this case not even yet employees.
The answer to your question is that there is no question - they have offered you nothing.
A "Term Agreement Letter" has no connection whatsoever to an offer.
You can and should take other jobs and not even alert them to the fact that you've taken a different job. Note that if they decide to hire someone else, they probably wouldn't even do you the courtesy of dropping you an email that they hired someone else.
The notion that there would be "bad feelings" from the people at this company is risible. At the very most, if anyone even noticed, some HR person there would think to themselves "Wow, one of the fools we handed out a snicker 'Term Agreement' to, realized it was BS."