Never had to do it myself, but I’d try sprinkling a few grains of powder through the nipple if I was in a hurry to get it out. Pretty sure Thompsons got a patent breech like most every percussion Hawken-type rifle.

This means the flash channel from the nipple makes a right angle turn to the center of the breech face so any powder you sprinkle down the nipple vent has to be below the stuck patch.

By way of comparison the vents on my flinters open through the side of the barrel at the breech.

"...if the gentlemen of Virginia shall send us a dozen of their sons, we would take great care in their education, instruct them in all we know, and make men of them." Canasatego 1744