What's the best way to handle feedback from agents and producers when submitting your screenplay?

Biggest thing to learn, in my experience of dealing with writers who have had feedback from industry people and also as a consultant who daily gives feedback on tv series, is that a note is a chance to learn and improve. You may not agree with the reaction from your reader, in which case, consider it objectively if you can. If there are similarities in the notes you are getting back, then this is a massive red flag and means you need to fix the issue that keeps surfacing whether you agree with it or not. The process of writing good television is both a creative and a commercial enterprise and both elements of your work need to sing together. Notes are often about what is making the work not commercial, so pay careful attention to that.

Treat feedback like gold-dust. Like any script notes, note everything down, give it a while for you to think about. Often the direct points in the notes are not correct - but really importantly they will flag up some flaw in the scene/ project. Always important to give time to consider the feedback - and not just react. So often we can find more creative ways to look at our work, perhaps more visually less on-the-nose scenes. This way the producers/ directors/ agents know that you have taken their advice on board - even if it's eventually rejected. Often other opinions can give a valuable insight into the work - even if at first they might seem anodyne. Film and TV are a collaborative purpose but your vision is essential.

Not all criticism gives you the right pointers what to do next. But it's mostly a good indicator of problem areas particularly when criticisms come up repeatedly. Develop an understanding of their perspective, are they good for early feedback on creative/mad ideas, or would they expect to be consulted on work that is almost ready?

Apply feedback that you feel is beneficial to you. It is important to remember that everyone's opinions are subjectives, and they are just opinions. You want to ensure you are telling a story you believe in. However, if you are looking to just sell your screenplay and your goal is to sell it - if that feedback is the sure route to get it sold, then it may be more beneficial to apply the feedback to sell the screenplay. Like with many things in this industry, it really depends on what your main objective is. Apply feedback accordingly to your goals.

Social media is very helpful to stay in touch, keep you aware of developments at their end, without being intrusive. Also sharing and commenting their stuff can establish a comfort zone of common interest.

Remember to ask what they are working on, perhaps this opens an opportunity to collaborate on other assignments besides you passion project - obviously they are sufficiently impressed to keep a dialogue with you.