sudomod

When I removed the voltage regulator off the adafruit screen, the solder peeled right off. I tried soldering it but, it does not seem to stick.

Assuming you haven't burnt the pads of, you'll need some flux to clean that up before solder will stick.

if the pad is gone then you need to trace where it went to and scrap the surface to solder to that instead

as camble suggested, clean it up. from the pic the GND pad looks like it is gone so you will need to scrape away the solder mask indicated in the pic below (be careful and make sure you stay away from that resistor), you can use a small flat blade screw driver to gently scrape and when you see some copper (enough to solder wire to) stop scrapping, flow some solder onto it and attach your GND wire, use hot glue to secure the wire so it doesn't rip off