I’m playing a grappling Eldritch Knight, and wanted to know if advantage on Strength checks (from the enlarge/reduce spell) would make my grapple check - which is an Athletics check - have advantage.
Advantage on Strength checks gives advantage on grapples
The rule for grappling says:
...you try to seize the target by making a grapple check instead of an attack roll: a Strength (Athletics) check contested by the target’s Strength (Athletics) or Dexterity (Acrobatics) check...
Enlarge gives advantage to all Strength checks, which include Strength (Athletics) checks.
A Strength (Athletics) check is, in fact, a Strength check - the hint is in the word "Strength".
If you are initiating a grapple then a Strength (Athletics) check is what you use and if you have advantage(disadvantage) on Strength checks you have advantage(disadvantage) on this check because, as pointed out above, its a Strength check.
If you are trying to avoid or escape from a grapple then you can choose to use Strength (Athletics) or Dexterity (Acrobatics). The first is a Strength check, the second isn't - its a Dexterity check. As a quick aside, Initiative is a Dexterity check so advantage(disadvantage) on Dexterity checks gives you the same on Initiative rolls.
If you are keen on building a grappler, you should check out the Grappler's Guide, one of the prime things it recommends aiming for is access to the Enlarge spell, partly to get the advantage you identified but also to allow you to grapple Huge sized creatures.
I believe so
When you initiate a grapple, you do so by:
... making a grapple check instead of an attack roll: a Strength (Athletics) check contested by the target’s Strength (Athletics)
Meaning that advantage on Strength checks does give you advantage when trying to grapple.