I have an old golf towel clipped on to my shooting bag. As mentioned above, it's been there for years, and is really just for wiping dirt or grease on.
I also carry one of these Amazon bulk towels, they are cheap, (12 towels for 20 bucks) and I carry it in the outside pocket of my shooting pouch. It is for wiping sweat off my face. I let my 12 and 20 lay when shooting a tournament, so no worries about space in that side of the pouch. The 28 and 410 are small enough that there's still space, even with the folded up towel.
I take 4 or 5 to every shoot, and start each event with a clean towel. They wash real easy in the machine.
Amazon.com: Amazon Basics 100% Cotton hand towels for bathroom - 12 Pack white towel (16 x 26 inches) : Home & Kitchen
www.amazon.com