I'm a senior software engineer that works in a small group (4 other colleagues and one immediate manager to us). For an R&D project, we work with a contractor to develop some software tools and do some research and development for a software that is going to be incorporated into our future product.
The area of this specific project is my immediate expertise; although my manager is pretty familiar with the topic, he is not necessarily an expert in this area. I'm the main point of contact between the contractors and the product owner and my manager.
The result of each sprint is presented in biweekly meetings to our group (me + my 3 colleagues + my manager, we are all senior software engineers).
There is a crucial tool that needs to be developed in this project and there is an issue with the current implementation by our contractor. I did some tests and I'm pretty sure that I know what the problem is and how to resolve it. In order to show the feasibility of my solution and demonstrate that my idea could indeed get rid of the current issue, I created a Jupyter notebook and send it to our contractor last week to possibly use it and hopefully they could build on top of it to get rid of the issue.
Today, in our sprint closure meeting, the contractor team acknowledged that they got my notebook and that indeed it solves the issue that we are facing in our current development. After that, when they jumped to presenting their results, they still showed results that were produced by their old implementation. I asked if they got the chance to incorporate my notebook into their current workflow, and they respond that: well, while my solution seems to work but they prefer to stick to their original implementation without giving clear explanation why.
I don't want to look like someone that is pretty picky, but my main concern as the main point of contact for this project is that we won't be able to reach the project's goal without resolving that issue and my manager also has the same opinion. I set up another meeting this week to discuss this issue further and possibly dive into more technical details to get to the bottom of this problem, but my main question is: how can I make sure that our contractors incorporate our guidance into their development without being rude or looking as someone that is too picky?