I know this not a good idea to check after the fact, but I thought I'd run this buy everyone to see if I did any damage. I recently mounted a Mark 4 Leupold (30mm tube) in a set of ARMS #22 rings. I tourqed the ring cap screws to 25 Inch pounds. After some reading I'm worried that I might have gone too tight and shouldn't have went tighter than 20 inch pounds. Do I have anything to worry about with 25 inch pounds on narrower rings like the ARMS ones? I just don't want to have damaged the scope in any way. Thanks.

I think you will be fine but...

There are a few variables depending if the rings are aluminum or steel, and who the manufacture is.  Most companies recommend 15 - 20 inch pounds, but Warne recommends 25 inch pounds.  Some companies say until the rings are tight and give no specs.  I know this does not answer your question, so If you are concerned why don't you call or email Leupold Customer Service.  They have always been very quick in answering my questions.

Maybe calling ARMS would be better to contact since this is their mount.

No matter what now, zero and shoot.

I did contact Leupold and they didn't seem to think it would be an issue. The rep said they typically recommend about 22 inch pounds. I think I figured out where I got the 25 inch pounds thing from. The instructions with my ADM mounts say 20-25 inch pounds and me being the tightness nut I am chose the high end of the spec. In the future though I'm thinking if I'm not given a spec I'm just going to stick with 20 inch pounds at the maximum to be on the safe side.