I have an aunt who is waaay more well-off than me. She's retired, no children, received inheritances, pension and travels the world. I am raising a family on a single, but decent, income (we don't have the latest and greatest but all our needs are met).
She frequently asks us to accompany her to this or that function, we pay for ourselves 90% of the time and it ends up costing for myself + 2 kids (and husband if he comes along). Recently I've begun declining more and more often due to eroding finances.
The phrase I used just yesterday was "How much are the tickets? I have to see if it works for this weeks budget." This made things clear to both of us. We didn't end up going as it was too expensive.
If I were you I'd say "Getting together would be great, but dinner at X is out of our budget. Can we eat at BK or somewhere cheaper?" (If she says "my treat" you may take her up on it and eat where she wants).