No, disadvantage on ability checks doesn't affect the fixed DC
If a vampire makes an unarmed strike attack and the attack is successful, it can choose to grapple instead of dealing damage. (MM, p. 297) Interestingly, the DC is already set as with other monster grapple attacks. The Vampire does not make a Strength (Athletics) check as is described in the Combat chapter in the Player's Handbook (p. 195).
So, the Vampire's grapple attack is a "monster grapple" with a set DC. The Vampire does not roll a Strength (Athletics) check. Also, remember that to break free from the grapple you can use either Strength (Athletics) or Dexterity (Acrobatics).
Escaping a Grapple. A Grappled creature can use its action to
escape. To do so, it must succeed on a Strength (Athletics) or
Dexterity (Acrobatics) check contested by your [or the Vampire's]
Strength (Athletics) check.
The disadvantage caused by the Hex spell will not improve the creature's chance to break free from the Vampire's
But... you could tackle this from other angles:
- you reduce the Vampire's chance to hit in the first place, e.g. cast
Protection from Evil and Good before
- you increase the creature's AC before facing the Vampire, again
reducing the chance the Vampire's attack roll is successful
- you improve the chances to succeed in the ability check, e.g. cast
Guidance or Enhance Ability (Bull's Strength)
- you provide assistance by using your action to Help, which
provides advantage on the Athletics/Acrobatics check to break free
I hope this helps.