I did something like that just recently. I was out of teabag tea and didn't want to go to the store for just one thing (as if!), so I took some scrap loosely woven nylon, cut it into circles and hemmed them, then made a big running stitch around the edge with embroider thread. I left the ends of that long so I could pull them and close my new teabag after I put in a bit of looseleaf tea. Better than a real teabag! I now use them over and over and wash them. Looseleaf tea lasts longer and has a better flavor, so I have the best of everything.
I got fancy after that and tied beads to the ends of the embroidery thread so they wouldn't slip back through the material.
Necessity is the mother of invention, they say!