I agree with MarkR (+1, by the way).
The application is on the client side...
So whatever web designers will try to do to stop some feature, they will either anger their users, have them hack away another solution, or move away to friendlier sites.
(I hate it when some broken down site needs me opening my Firefox debugger to enable me to complete my correct for just because some braindead developer forgot to declare his i loop variable and thus, making it a global... And I did it again less than two days ago)
As online apps should never rely on client-side controls and protections (i.e. testing the date value on client is a cool bonus, but testing it anyway and always on the server is the thing to do).
To the worst thing that could happen would be for the app to break on the GM user because of some faulty script. But from the server viewpoint, it should remain pristine.
... Thus, the client should be held responsible...
That means that whatever hack the user adds to his browser, the user is then on his own. At the very best, he/she could discover some hidden bug and report it. On the worst side, the site won't work properly
...Now, does it means client/server cooperation, too?
Most people using GM or whatever to enhance a site is showing that the site does not suit exactly is tastes. The good thing, like Rich wrote down, is that they are still on your site, and not elsewhere.
Either the "enhancement" is for his/her own very personal taste, and, hey, what's the problem if he/she wants to see your black-on-white web page with yellow-on-blue? Or perhaps the "enhancement" adds a lot of value to your site. In this case, I guess that what you want is to either offer the same features for everyone (thanking the author of the GM for his idea could be a good idea), or perhaps support it as an optional feature ("click here for advanced experience") or... an GreaseMonkey script?