My AmazonBasics laminator wrapped a small card around one of its rollers and jammed solid:
The lever sticking out on the lower right (above) drives the rollers in reverse by moving the motor from one gear to the other:
Obviously, reverse gear wouldn’t get me anywhere, but dismantling the rollers required cutting the junction between the heating elements running through the aluminum extrusions:
I spliced a few inches of wire onto those leads. If there’s a next time, I can cut the splice in the middle and use a wire nut.
The white plastic curl in the lower right showed they ran a deburring tool around the exit slot and called it Good Enough™.
The gears slide off the roller shafts and the rollers out of the extrusions, after which removing the tightly wrapped and completely useless card posed no problem.
One lone, short, and eagerly self-tapping screw holds each plastic end plate to the extrusion, so be careful about cross-threading.
All in all, this was easy enough, although I’m sure I was supposed to just throw the laminator away and buy a new one.
Update: If you dislodged some of the wires, a few more pix of the interior may come in handy.
The Smell of Molten Projects in the Morning 
You are a frustratingly poor consumer by fixing things and not consuming them. 😉
Well played, sir!