Q: When an engine is replaced should it include a new intake boot or air intake system? Or is that separate?

Last year I had my engine replaced with a refurbished one. When I drove off the lot, the car stopped accelerating. Learned that the throttled needed to be tightened. Just recently, 4 days after putting car in a different shop for a replaced ignition switch, the car experienced same systems as loose throttle. I noticed the car had been tampered with, I guess the technician was examining the car to discover the problem, and I noticed that an electrical wire that connects to phone was cut. I also noticed the car shook slightly after I drove off, and I thought it had something to do with him putting the car back together after the repair, and that it would clear, but 4 days later the car just stopped, couldn't accelerate. Put the car back in the shop and finally a week later they tell me I need a new intake boot and they're charging me for it. I don't think I should have to pay, and hoping it's covered in warranty, but want to know if it's considered part of the engine.

My car has 120000 miles.
My car has an automatic transmission.