aside from going against your mother's wishes...finishing the quilt depends on the age of it.
if you do not have the same era of fabric, then it will look ODD when finished.
If it is really old/vintage, then the historians say DON'T finish it. But keep it as it with a label attached to it giving the history of it.
as for FRAMING a block...please don't. Cotton is considered a living fiber and once it is encased in a frame it will dry rot and be lost. Make your mom a small pillow out of it, or a wall hanging!

If you really want to finish the quilt talk to your mom and tell her you feel almost like you are being asked to finish it (isn't that kind of the way you feel about it?). Tell her of your love for your grandmother, and that you want to respond to that love by finishing the quilt. And mention also that you treasure the family history involved and want to pass that on. Bet your mom will respect your feelings and relax.

I say, finish it, just like your grandmother was trying to do when she died. She wanted that quilt finished, so go for it! Enjoy the process, & I bet you will think of her everytime you work on it, & look at it later! Enjoy the journey!...

I think you should finish it. Grandmother would be pleased!

I would finish and cherish it.

Superstitions don't work with quilters. Sounds like this quilt is 'begging' to be finished. Go to it.

Finish it, I wish I had something handed down that my Grandmother either did or was working on. I remember her talking about quilting bees but they did all their quilts for the church and I never did see any of them . I am the only one in my family that quilts & my grandchildren love receiving them. My youngest gs (age nine) has requested that I make a baby quilt for him for his child when he gets married and starts a family. I want to first make each of them one for graduation from high school. Keep us posted on your decision but it seems unamious that you finish it.

Would it help mom if you passed the quilt along for someone else to finish it?

She should finish it... Gramma would not have started a quilt if it wasn't going to be finished.And I'm sure she will be smiling down on her Granddaughter

Do you dictate your own heart!
If you generate anxiety in some way ... will not help anyone!
It would be nice to her mother when she feels the time is, make a part and you finish it. So would a quilt of three generations! And they will all be happy!
Good luck!
A hug!