Hopefully this is not too late since you posted yesterday. I disagree with the replies saying "fix the leak" when you say it's not leaking. If it's outer of a dual setup, that reduces your chance of problematic failure. Test it with soap solution when inflated to max allowable pressure printed on sidewall. That'll be higher than service pressure. Apply with a small clean acid brush. Leave undisturbed for an hour in the shade (so soap solution doesn't evaporate) with the problem exactly at the top, ie. 12:00. If no bubbles I wouldn't try to fix anything, I'd just keep an eye on it and test pressures frequently until you gain confidence it's not going to lose air. If you really want to be thorough about it, break the bead and carefully inspect the inside of the tire in that area with a flashlight. If no penetration, you're done, reseat the bead and breath easy. You could pull out the piece of plastic (as you describe it) so as the tread wears down, the pressure of the road won't push the plastic deeper into the tire. Then retest with soap solution same way as above. If by some strange chance it now leaks, then patch it. If it's penetrated, definitely pull it out and apply a patch. To achieve success with a patch, there are several key steps you must follow religiously. This may be overkill but it's always worked for me. First of all, you're lucky it's in the tread. Never try to patch damage beyond the tread area going up the sidewall, it flexes too much and patch isn't likely to hold. Next, roughen the patch area with the metal tool of patch kit or sandpaper 100 grit or coarser. Spend plenty of time doing this carefully. You're getting down to virgin unoxidized rubber. Blow dust away with compressed air. Next, wipe with a little acetone, lacquer thinner or MEK several times with new areas of the clean rag or paper towel. Let dry. Blow once again with clean dry compressed air. Apply rubber cement, let dry and peel and apply the patch. Press thoroughly paying attention to the center where the penetration was and work outwards getting all edges. I'd never bother to do as some said and use both plug and patch. I don't like enlarging the hole with the plug rat tail rasp tool. As one poster said, plugs have a reputation of not working all that well. Was in the tire business starting 1972 for many years and never had a patch fail done this way.