That just happened to my sister last month, except it was $250. She just said "I am not paying for that". The only thing that works for me is endless patience and the willingness to just walk out.
Wow, I'm really sorry this happened. I read that it can disappear over time, but that varies. I really hope this happens to you. It sounds like such a pain.
Super bummer. They look a lot like American dog ticks, but have much longer mouthparts and tend to be larger. You guys be on the lookout for these. They have a very painful bite.
Look in the areas with tall grass for the larvae, and in dead and rotting organic material (especially logs) for adult mites. The adults live close to the ground and are readily visible with the naked eye.