Exhaust is in the Air

My 2002 Honda Civic LX has been having a problem with the air system. When the air or heat is not on recirculate, the car smells like exhaust. It started happening at about 100,000 miles, and now it is at 250,000 miles. The air system has been flushed and the air filter has been replaced. The mechanic recommended a replacement catalytic converter. First, in an effort to save money, I tried a refurbished one. The same problem still occurred, so we got a new certified Honda catalytic converter from the dealership and had them install it. Goodbye $850. It happens at all temperatures. The exhaust system looks to be okay. What is wrong, and how much will it cost?

I think you need to find a more competent mechanic.
And that more competent might use a evap/smoke machine to locate any possible exhaust leaks.
It’s not always necessary to bust out that too, but it does sometimes help.
Leaking exhaust manifold gaskets or exhaust manifold flange gaskets come to mind.

Outside air is brought into your car through the grill between your windshield wipers…This is the highest air-pressure area on the car body, selected to avoid the problem you think you have…Even on “recirculate”, SOME outside air is blended in…Exhaust leaks under the hood can sometimes find their way into the heater air intake, or maybe it’s just the cars in front of you…