The masking is really just to keep burned soot from settling on the wood, and you won’t get any actual scorch marks or damage to the areas you didn’t engrave. Some unsealed wood can be tough to clean and it may get stained when you rub the soot, so it can be useful with that material. But when it comes to finished wood, I embrace going maskless 75% of the time. (And it’s much safer to go maskless too.)
And there’s no way to know if stronger masking tape would stick to the finish, but I’d guess not. (And using something that doesn’t stick super well is a big fire risk, and not worth trying.)