After Hazel runs, have it NOT change modification date?

I have Hazel doing a very nice action of adding certain wording into the comments section of a file, BUT it changes the modification date of the file. Is there a way to keep that from not happening? Otherwise it changes those dates to today.

There's no way around that since the OS will update the time when you change that information. You can write a script to change the modification date back, though that would require you to also record what that date was beforehand.

Any script ideas on how to grab the time/date first then run Hazel then finish script?

I suggest researching how to do shell/bash scripts. I'm guessing you want to use some combination of the "ls" and "touch" commands.