Can someone please tell me how to remove a screw with a hopelessly stripped head from the barrel band of a Marlin 336. It is pretty badly buggered and I can get no purchase with a flathead screwdriver. All of the screw extractors I have seen look too large, and I am hesitant to spend the money on something I am likely to only use once.

It's not causing any problems other than looking ugly, but it bothers me. Any help appreciated.

I am not completely familar with that particular gun....but:

Is the other side of the screw out in the open? If the other side can be seen, use a drill and a small drill bit.....drill into the center of the screw and is should screw it out from the back. Does that make sense?

Tap the center of the small "other end" with a punch and drill it.....it will work.

If the opposite end of the screw is not exposed....forget everything I just mentioned

Left hand drill bit or.

The Grap-it screw extractor works nice.

HK Dude.   The other end is exposed, and what you said makes sense and I'm thinking it might work.  The path of least resistance for the screw would be to unscrew rather than yield to the drill bit in it's valiant effort to pierce the screw.  And It doesn't seem to be in very tight,  I can turn the screw clockwise, and back to the starting point counterclockwise.  

I may give it a try tomorrow.   Thanks.

Did you get it out?

A small chisel (or punch) and hammer is all you need. Catch it near the edge and tap, rotate around the head as it binds up.

First thing to do is get a brass drift that about covers the head of the screw and give it a few stout "wacks" {make sure you got things supported well}
This should "break" it free.
Now, if you can in anyway use a drift to "hammer" the edges of the screw slot back into shape enough to get a bite on it.
If you cant.
Use a engraving tool (air is best, but electric will work) and set it on a lowwer setting and try working the screw out using what is  left of the slot "sholder" as a back drop for the engraver.
The vibration will work the screw out. If it doesnt break free, wack it a couple more times with the brass drift to make sure it is "broke"free.

Just remember that you are smarter than the screw, and it aint gonna beat you. (thats what I always tell myself anyway)