The size of this comb is probablly drone comb size. A common trick of beekeepers in the past has been to put a small or medium frame in the deep brood box to have the bees build drone comb off the bottom bar of the small frame. They fill the space under the frame with drone comb. The subsequent drone that fill these cells can now be checked for mites and cut off the bottom of the small frame and frozen or discarded. Current thinking for IPM (integrated pest management) is now that this is not enough. That there should be two deep frames of drone comb in the hive (assuming a two box hive, one frame for each box) that should be frozen or cut out and discarded once capped. This will kill all the mites which like drone better because they take 3 more days to develope so the mites have 3 more days to lay eggs.
So here is my opinion, wait untill your free hanging comb is capped and then cut it off and either check it for mites or just discard it and put the other frame back in. My hives have two deeps of drone comb which I put in positions 3 and 8 in the brood box, I paint the top bar of the frame green to distinguish it from the rest (make it easier to see) and remove it and freeze it when it is capped for IPM. I don't put insecticides in my hives to kill mites. Good luck!