Advice? Chalice recession

I've never heard of chalices being sensitive to injury, are they? I recently purchased a mummy eye chalice locally and the drag had a pest anemone on it. I cut that piece of rock off prior to putting it in my tank, but the rock chip extended a little under the frag when it broke free. Only a very tiny bit of flesh ripped off (1/8 in x 1/4 in roughly), but the wound is growing. Anyone have experience with this? I'd not have thought it would have really affected it.

Attached is a pic. Top part, you can see skeletal ridges. The wound went from being about an 1/8 inch off the side to almost 1/2 inch into the frag. I'd rather not lose it.

 

I don't have lugols, but I did a Coral Rx dip last night. See how it goes... Thanks Jeremy.

The super glue, do you cover the top of the coral along the spot or try to just get it along the edge? 15 years in this hobby and I've never experienced this.

 

It was still on the move, so I did another dip, tried to clean up the dying tissue, and ran a line of super glue. Fingers are crossed.