Merits in Avatar Magical Attack and gear that specifically enhances avatar magic attack will increase the damage.
Avatar's TP increases damage and is completely consumed by the successful use of this Blood Pact.
The phases of the moon also modify the damage (bonus is consistent throughout the duration of the phase):
Full Moon: No damage bonus
Gibbous Moon: Low damage bonus
Half Moon: Medium damage bonus
Crescent Moon: High damage bonus
New Moon: Maximum damage bonus
Trust: Karaha-Baruha can use a weapon skill of the same name when he has at least 1000 TP. He does not summon Fenrir to use it. It is unknown if Trust: Karaha-Baruha's version is affected by the moon, but it appears to have skillchain properties, unlike Fenrir's blood pact.