Edward the Eldritch Knight can make a Weapon Bond, he can summon the weapon and it will teleport to his hand.
The Monsters Manual indicates that claws are natural weapons, and that natural weapons are weapons.
When Edward summons his claws, does the cat teleport with them?
MELEE AND RANGED ATTACKS The most common actions that a monster will take in combat are melee and ranged attacks. These can be spell attacks or weapon attacks where "weapon" might be a manufactured item or a natural weapon such as a claw or tail spike. (MM p10)
Weapon Bond At 3rd level, you learn a ritual that creates a magical bond between yourself and one weapon... If it is on the same plane of existence, you can summon that weapon as a bonus action on your turn, causing it to teleport instantly to your hand. (PHB p75)
Cat Claws. Melee Weapon Attack: +0 to hit, reach 5 ft., one target. Hit: 1 slashing damage. (Basic Rules p121)