I have not found that it leaves a mark. If you use really sticky tape it can leave stickiness, but that wears off after a little bit. The best way to resolve that seems to be moisturizer (i tried nail polish remover, alcohol) you don’t have to tape your whole mouth, you can just tape the middle. Whatever you like best. I found gentle post-surgery paper tape that works really well, doesn’t leave residue and comes off easy.
Tell me how it works for you, I’d love to know if it works for other people. After trying it I can’t figure out why it’s not super-common. My husband tells me sometimes I snore a little through my nose, but nothing at all like before. Also, I will often use a breathe right strip at the same time to open up my nose.