How to re-fold paper cupcake liners?
Maybe try reshaping a whole stack at once.  

You might slowly bend them back into shape by hand, holding the stack and in place with your thumbs and wrapping your fingers around to bend the edges of the circle back towards the proper shape.  Only the top one or two liners might fold in towards the middle, because the liners would layer together, and make the stack as a whole less flexible so there isn't room for the middle layers to fold in - and you can gently reshape them and distribute the pleats on the top few as you're bending, because even if you wouldn't want to do so for every liner, shaping the whole stack at once is a lot less time and a lot more done at once.

Alternatively, you might set a stack (or partial stack) on top of the muffin tin, and weigh them down.  If you have a second tin, or individual silicone muffin cups, or a stack of liners that are still the right shape and well wrapped, you can set that on top, with extra weight if needed, and let them get pushed down into the muffin tin.  The less weight and more time it takes will probably give a better result (since the reshaping is gentler) but it's up to you how neatly you want t done.  You might still get smaller pleats out of place, but overall the shape should match the muffin tin fairly well.  This can also be done with nestling round cookie cutters - the point is to brace the inside with something rigid so it doesn't have room to just fold in.

Or something in between, brace the inside of the liner stack with something of the right diameter, flip it upside down, and smooth your hands down the stack to slowly narrow the diameter back down.  you can leave them in between sessions, or use a rubber band (once they're shaped enough), and let them settle back into shape by themselves.