As promised, here is my version of a felt tea bag.
*white six strand embroidery floss
Start with a rectangle of white felt about twice the width and slightly over twice the length you want the finished tea bag. (Mine is a bit squat, because I was trying to get the most out of a sheet of felt.) Stitch the longer sides together using a whip stitch. These stitches won't be seen, so no need to be terribly careful.
Flatten the tube you've just created so that the stitched edge runs down the middle.
Fold the flattened tube in half lengthwise with the stitching on the outside.
Stitch a line just below the folded edge.
Fold the sides up so that both stitched edges are on the inside.
Cut pieces of scrap felt into small bits, I used green, and stuff them (with or without the cat hair) into both open sections.
Cut off the corners of the top edges.
Stitch all four layers of felt together at the top along the cut edge until just before halfway. Tie a knot in the end of a length of embroidery floss, and thread it through the top center of the two innermost pieces of felt, making a couple of stitches into only the two inner layers (see photo). Finish stitching up the top.
Cut a rectangle of green (or any color, really) felt, that when folded will create a square. Bring the other end of the thread attached to the top of the bag up through the middle of the small rectangle and tie a knot in the end. Stitch around the edges (you could add embroidery, like a tea leaf, the word tea, or an initial).
Adore your handiwork.
If you make one, I'd love to see pictures. I ask only that the above information is not used for commercial purposes. Enjoy!