If I attach scripts to an object and remove their old script, the game won't recognize that the object has a new script on objects that are already placed in the game.

For example, I'm trying to replace the script attached to hawks.
If I do so and load up the game, the hawks flying around Solitude still have the old script attached to them.
However, if I use the console to spawn a new hawk, that hawk will have the new script.

So how do I make the existing hawks have the new script instead?

I can edit the original script to get the effect I want, but there are other objects that use that script too, so I'd rather leave it alone and use a new script just for the hawks.

I also tried using the new script to extend the old one, but the existing hawks still don't have the new script attached in the game.

I think you need to call "Reset()" on every single hawk.