The fabric looks to thin for a bag, or a quilt. Thin fabric will loose its shape easily.

I would not cut it up and make it into a lap quilt.

quilt it and put it on the wall !

You could make an apron with it. TipNut.com has many patterns for making aprons from tea towels.

i would get a cheap canvas that is the right size and just stretch it over that and staple it on the back.

I wouldn't use it for a bag because it looks very delicate. I would probably put a very flat backing and make a wall hanging, or put it into a poster frame. On one of the blogs I read, Casey (blog owner) has a vintage handkerchief mounted on a white board with magnets (prevents having to pin into it). You can see it here: http://blog.caseybrowndesigns.com/20...lections-four/

Not sure how big your piece is, or whether this would work, but I thought the idea was fabulous and plan to mount some of my own vintage hankies this way!

quilt and keep...too nice to cut up... or could you back it, fold it and stitch sides to make a big bag?

vintage tea towel
 

It looks very fragile. If you truly want to preserve it I would suggest having it custom framed.

I think I would put it into a wall hanging so you could always see it.

Make it the center of a quilt like a panel and putt the co-ordination fabrics from that. It would be beautiful, I would love to see what you come up with. Good Luck