Glue residue is stuck on digitizer screen

I think we need to get our terminology straight here. The iPad mini has a digitizer (the part you touch) and an LCD (the part that shows the image).

Why was there warm glue anywhere near your iPad and what exactly was the warm glue on; the LCD or digitizer?

The proper way to re-assemble an iPad is to use adhesive strips. You need to clean off the old adhesive from the aluminum frame with IPA so that it sets correctly. If you are using a new digitizer, some of them come with adhesive strips pre-installed. They aren't the greatest but not everyone wants, or can buy, separate high quality adhesive. I recommend this adhesive.

Now, if you have glue on the digitizer, what you need to remove it depends on the type of glue you used. If it is epoxy or super glue, try acetone. Whatever you do, don't scrape or you will scratch the surface. If the glue is on the LCD, you are probably in trouble. Acetone might work but don't pour acetone (or any liquid) directly on the LCD. Use a very soft cloth. The problem with the LCD is that the surface is very delicate.You will likely scuff it or damage it by trying to remove the glue. Also be very careful with the black, cloth-like edges of the LCD. That's where a lot of the internal wires run and they are easily damaged.