Do not unclaim the griffin it cannot be claimed again but if you unclaimed it already or by accident then try this

First knock out the grifin then tame it again after you have tamed it you will have to chronical it because if you don't it will die from neglect in 15 mins after you chronical it the effect of it dying from neglect will go away and revive it in one of the obelisks and you got your griffin back