There is an alternate version of S.T.A.R.S. outfit in which Jill is seen without a beret hat on her head. However, in this version, she is wearing a different outfit that doesn't have a beret hat either. In fact, this outfit is for the most part the same as the normal one, with the only difference being that the missing headwear.

So if you are a fan of the game, and you don't like the beret hat, you can easily remove it from the costume by installing this mod! The only thing that you have to do is to open the file in your computer.