Do leave the mission. Instead, as soon as the XP pops up on your screen, completely force-close the Hitman 3 application via your console dashboard or by hitting Alt+F4 on PC.
When you reload the game, you will be back at the safehouse with all the massive XP you just earned, but the mission will be reset!
Prestige Objectives are the single greatest source of Mastery XP. Always select one before leaving the safehouse.



