Homebrew
Keen Sight
The gryphon has Advantage on Wisdom (Perception) checks that rely on sight.
Happily Mounted Takes 1d4 less damage from attacks while its owner is riding it
Companion's Bond Once per Short Rest, the gryphon can gain 1d10+5 Temporary Hit Points if it plays, snuggles, or has some sort of loving interaction with its owner for at least 15 minutes.
Multiattack
The gryphon makes two attacks: one with its Beak and one with its Claws.
Beak
Melee Weapon Attack: +5 1d20+5 to hit, reach 5 ft., one target. Hit: 1d8+3 piercing damage.
Claws
Melee Weapon Attack: +5 1d20+5 to hit, reach 5 ft., one target. Hit: 2d6+3 slashing damage.