I'm guessing by "mediating particles", you don't mean those affected by fields, but rather those 'propagating' the field, i.e. photons.
And well, my research tells me that photons don't really exist. 🙃
Well, particles don't really exist, in the traditional sense. They're not solid balls flying through space. They're rather just peaks in the EM and gravitational fields. And then, if you've got a disturbance in a field, a peak or wave will travel along the field, which propagates that disturbance. And if you've got all that internalized, then you could call that peak/wave a "particle" again.
Here's a rough source / different explanation of those claims: https://physics.stackexchange.com/a/201
But yeah, I don't think this particle analogy is helping us here. We're ultimately still just talking about a field being affected by gravity.
(Still, thanks for the input. I'm sorting my thoughts as I go, and reading that I've also been subjected to an unhelpful analogy is helping it make sense.)