What is the term for replacing one word/phrase with one that is more friendly/appropriate

Solution 1:

Perhaps you are thinking of the word euphemism, which has senses “The use of a word or phrase to replace another with one that is considered less offensive, blunt or vulgar than the word or phrase it replaces” and “A word or phrase that is used to replace another in this way.”

Some words that are related to the topic (but probably don't quite fit the context of the question) are bowdlerize (“To remove or alter those parts of a text considered offensive, vulgar, or otherwise unseemly”), gentrify (“to renovate something, especially housing, to make it more appealing to the middle classes”), and expurgate (“To edit out rude, incorrect, offensive, useless, or otherwise undesirable information from a book, CD or other publication; to cleanse; to purge”).

Solution 2:

I think moderate is the most apt term here as it essentially means what you are asking for. Censor is another word, but is more about hiding words than "moderating" them.