Opposed checks use Ability checks like STR (Athletics).
Saving Throws are for resisting a fixed DC effect.
I don't recommend using a Saving Throw for an opposed check.
The house rule would remove the opposed check from Grapple and exchange it with a skill check. The DC would not be considered a Shaving Throw even if its formula replicates a Saving Throw one.
I am currently experimenting with the following change: The target resisting the grapple has the choice to roll or take 8. If the target resisting the grapple has an advantage or disadvantage to resist a grapple and takes 8, it must add or subtract 3.