The advantage of the teabag paper is it can be left in and doesn't need to be torn out.
For cheap abundant "make sure you tear it out" use in my sewing supplies is parchment paper I get at the dollar store (1 x 25 foot). It is not coated, can be ironed and is easily seen through. Sturdier than tissue paper but still easy to tear out. But then again there is still the tearing out...
I haven't looked at this project, is it something better done on a foundation or would it be ok doing it tear out or the folded paper technique of paper piecing? If it is best left on the foundation, I would look at something like the teabag paper. If it is a wall hanging and you aren't the type to ever wash it, leave it in. Then if you do have to wash it, just be gentle.and it should be ok but the more you agitate it or tumble it, the more the paper will be rubbing.