No, Touch of Moonglove does not need another 'this turn'
Theoretically, damage dealt by a source to another source can be remembered across the game, because it's part of the game's history. However, for practical reasons, no card references damage dealt in previous turns without a system (e.g. counters), because it would be a large impediment to the game if players had to keep track of all instances of damage, even if they knew beforehand they might need it later.
The only exception is commander damage to opponents, which is remembered for the whole game, but only because every player knows beforehand to keep track of that damage, and it's only one card per player.
Wither and infect are kind of remembered through -1/-1 counters, but those don't count as "remembered damage". The counters could come from anywhere, could be removed, and, most importantly, those counters are damage results, not the actual damage:
119.4. Damage is processed in a three-part sequence.
119.4a First, damage is dealt, as modified by replacement and prevention effects that interact with damage. [..]
119.4b Next, damage that’s been dealt is processed into its results [..]
Marking damage on a creature is also a damage result, not the actual damage.
