My Beast Master Ranger player is looking to use his hunter's mark bonus on his animal companion's attack action. Is the hunter's mark damage bonus strictly only for the ranger's attacks, or since the ranger is using their Attack action to command their animal companion to attack in their stead, can the animal companion get that bonus?
Only for the Ranger's Attacks
Hunter's Mark is cast on an initial target and provides a bonus on the caster's attacks. Emphasis is mine below:
You choose a creature you can see within range and mystically mark it as your quarry. Until the spell ends, you deal an extra 1d6 damage to the target whenever you hit it with a weapon attack, and you have advantage on any Wisdom (Perception) or Wisdom (Survival) check you make to find it.
Just like the extra damage doesn't apply to your allies, it doesn't apply to your beast either (which is effectively another creature and an ally). It is for your attacks and your attacks only.
I'm gonna say No, the animal companion can't claim the bonus damage. Hunter's Mark says...
Until the spell ends, you deal an extra 1d6 damage to the target whenever you hit it with a weapon attack, (...)
Emphasis mine. You, not your allies or friendly creatures or mutual enemies. You, the caster of the spell.