When a character is removed from play by Mace's ability, it leaves play as normal: any non-terminal attachments on it are returned to their owner's hands, any terminal attachments and tokens are discarded, any lasting or delayed effects affecting it expire. At the beginning of the next phase, that character enters play under its owner's control, standing.
If the character removed by Mace cannot re-enter play for some reason (for instance, because a copy of it is in the dead pile), that character remains removed from the game indefinitely. Barring the Gates and The Iron Bank Will Have Its Due will not prevent characters removed by Mace's ability from re-entering play. (Source.)
Unlike the original version of the card, the Reaction only works with unique characters, and it puts power on the character that enters play rather than on Mace himself.