Do the same caveats apply to removing a person from, as adding a person to, a deed if there is a mortgage lien?

Welcome to AMHD. An owner of land, whose name is on the deed, is not actually 'removed'; the owner 'conveys' his interest by deed, such as a quit claim deed or warranty deed. If there is a mortgage, then read through the paragraphs to see whether there is a 'due on sale' clause; if there is, the 'owner' may have a problem conveying his interest, even if there is not an acutal 'sale'. You will need to read the language and figure out what it means.