Repair REMOVE GLUE ON FABRIC

I have never tried to do this but can you find any info on whether the goo gone product would work on fabric?
The glue probably needs to be dissolved with a solvent that will not damage or discolor the fabric. Unless it was a heat set glue in which case you might be able to heat it again to remove it. Perhaps similar to the technique you'd use to get bubblegum residue off fabric?

 

I would maybe try white vinegar or maybe these carefully on a cotton swab and than wash fabric with water:
Goo Gone
Stain remover for clothes
100% Acetone for nails

 

Having used goo gone I can say it's a very greasy product so might not be best on fabrics (label says for carpets & clothes but do not use on silk, leather & suede). There are some products (i.e satin devil) out there that are designed to remove substances like glue from fabrics that might safer to try. Also depending on the glue, it may have affected the fibres of the fabric underneath so may not be possible to remove it without leaving a damaged fabric patch.
It may be easier to sew some decorative fabric/trim over the glue or add some other decoration. Glue removal really depends on the fabric and type of glue. It would be a case of testing first if you can find some similar fabric to play around with!

 

Maybe test on the under side of the obi if it's the same fabric.
Be cautious with acetone as some fabrics react (melt away) if touched by acetone.
If it isn't hot melt glue, maybe start with a simple water soak? As others have said it all depends on what glue was used. Good luck!
Maybe a nice ribbon or cord wrapped around the obi & fancy knot would distract from the area?

 

If the dots of glue was hot-glue, you might consider putting the piece in the freezer overnight. Usually that hardens the glue more and makes it easier to pull off. Of course, this might pull off the surface of the fabric so the left over spots might be a bit fuzzy, but at least it's likely to lead to a clean break.

I hope this helps!