You should unclaim it because it will not die after 15 min. But it will become a real wild griffin and get angry on you.

then you can refresh your game if youre on singleplayer and knock it out again and tame it again, also any balms that you have used before will stay on the griffin when you unclaim it

make sure to chronicle the griffin nd revive once you have reached your satisfied level or else it will die of neglect

warning: max level is 600, it won't gain any more levels after that

note: if you refresh your game after you knock out an unclaimed griffin, it will revert to a wild griffin's stats instead of your griffins' stats