I learnt with my Kallah teacher that I have to always be really careful to take off any dead skin from my feet before going to Mikvah and that is what I did for the beginning of my marriage. However now I see that in Kitzur Dinei Tahara it does not mention to take off the dead skin from feet. Do we indeed have to be particular on taking off every little piece of skin?
You do not have to take off the dead skin.
However if you do want to take it off often (regardless of Mikvah), then you would have to do it before going to Mikvah.
שו”ע יו”ד סימן קצח סעיף כב
שו”ת שבט הלוי חלק ג סימן קכז. שו”ת משנה הלכות חלק י סימן קמא.