So I snipped a st and unraveled a row right where the heel began.
This is the second in the series of what to do with your hand-knit socks after they have worn-out soles. Here is a lovely sock in a mohair/wool yarn that I loved to wear. It was soft and warm and cuddly. Unfortunately, it developed a number of worn out spots on the heel. This sock was knit toe-up so the method I used in the cup holder won't work. You can't unravel a knit backwards. It will only unravel from the bind-off to the cast-on and not vice versa.
You can also knit on a thumb gusset and hand and convert them into fingerless mitts. In that case, I would do a blanket st or overcast st on the cut edge and tack it down to the newly knitted fabric. Embroidery floss is good for this as it is soft and you can match the cut edge color very closely. You may need to use only 3 or 4 strands of floss.