IF the solder can be re-heated with an Electric Soldering Iron, then PERHAPS (and I say perhaps) you can 'lift' the solder using a wet rag. BUT, I have to think that the solder will run 'down' if it's heated.
Consider pulling up on the solder and cutting under it with an Exacto Knife; NOT scissors. (It's a Graphic Artists' knife - VERY sharp!) You'll probably be able to notice the 'damage' once the solder is removed. But I have to tell ya - IF anyone was to come to my house, get on their hands and knees, and LOOK for 'damaged' carpet, AND find it, then they have WAAAAAY too much free time on their hands. (Plus, I'd never invite them back.)
I do wish you well. My best to ya and hope this helps.