The main problem with this phrase is that piece and peace are homophones. So until you read a phrase, you don’t know which one is used, or misused.
Say one’s piece is the traditional version of the phrase and means to give a prepared speech or share an established opinion.
Make peace means to let go of a grudge or reconnect with someone after an argument.
Hold one’s peace is to stay quiet about one’s objections. This is most often heard in marriage ceremonies.
An argument can be made for saying one’s peace after holding it, but it is more likely to be seen as a misspelling of the first idiom in this list.
To peace out is to leave a location or mentally leave a situation. This is extremely informal slang and should be avoided in formal writing.
Side note: there is an archaic saying to piece out something, which means to lengthen something or extend it.
So I said my piece, delivered my advice. [Irish Independent]
That bitterness drove Pacquiao to a nearly flawless record in America, with only one loss between 2001 and 2009, the year Pacquiao finally made peace with his father. [The Washington Post]
When King returned, Jennifer thought about saying something, anything, to her. Perhaps warn her against leaving with McKoy. But she held her peace and watched as the two walked along Williams Street and out of sight. [Jamaica Observer]
Garth Brooks peaced out of the country music scene in 2001, at which point he turned down millions in album and ticket sales so he could focus on his family. [Music Times]