Rules FAQ:
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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.
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Barring the Gates and The Iron Bank Will Have Its Due will not prevent characters removed by Mace's ability from reentering play. (Source)
- If the character removed from the game by Mace Tyrell cannot reenter play because another copy of it is in the dead pile, that character would remain removed from the game indefinitely. (Source)