Q:

Is Greater Restoration the only way to reverse Ability Score Damage?

Some monsters or effects can cause a character's ability scores to be decreased.
The Greater Restoration spell can end "any reduction to one of the target's ability scores".
Is there any other way to reduce or remove ability score damage in 5e?

A:

There are no generalised rules for ability score decreases, reductions, penalties, or damage. Every effect that reduces an ability score is highly specific, and sets its own rules and conditions. It might be worth mentioning that (as far as I'm aware), no such effect uses the term "ability score damage".
For examples, the Shadow can reduce Strength, and said reduction lasts until the target finishes a short or long rest.
On the other hand, the Intellect Devourer can reduce Intelligence to 0, and does not specify a way to regain Intelligence, so only effects like Greater Restoration that specifically remove reductions to ability scores would be effective here.
And for something completely different, the Feeblemind spell reduces Intelligence and Charisma to 1, specifying that the target can be fixed by making a saving throw, or any of Greater Restoration, Heal, or Wish.
So the short answer is that it depends entirely on the source of the ability score reduction. However, the only general solutions appear to be Greater Restoration and Wish.

A:

Xanathar's Guide to Everything (p. 131) includes "Relaxation" as an option for a downtime activity, which lets a character recover reduced ability scores by spending a week of downtime:

Resources. Relaxation requires one week. A character
  needs to maintain at least a modest lifestyle while relaxing to gain
  the benefit of the activity.
Resolution. Characters who maintain at least a modest lifestyle
  while relaxing gain several benefits. While relaxing, a character
  gains advantage on saving throws to recover from long-acting diseases
  and poisons. In addition, at the end of the week, a character can end
  one effect that keeps the character from regaining hit points, or
  can restore one ability score that has been reduced to less than its
  normal value. This benefit cannot be used if the harmful effect was
  caused by a spell or some other magical effect with an ongoing
  duration.

This is an optional rule, and isn't allowed in the Adventurer’s League.

