My 96 Accord has some mild front-end damage thats getting fixed within the next 2 weeks. The radiator is tilted at maybe 3-5 degrees towards the engine. Front subframe (maybe using wrong term, its the 3 piece metal bar that runs horizontally on top of the radiator) is torqued, a little twisted.

BUT...about 3-4 seconds after I take my foot off the gas, this horrible clicking, contact noise happens. Its incredibly loud. Like trying to start your motor with a dead battery...a starter noise but with more ...errr....bass? Its just when I let off the gas, shifting doesn't affect it, and it happens during braking too.

I'm thinking maybe a fan is blocked but from what I know, they're electrical, and doesn't correlate with the throttle. Any ideas? Also...who should fix it? A bodyshop or mechanics?

 

My guess is the lower crossmember is tweaked a bit too. It's pushed back a bit, and under engine braking or regular braking, the motor is perching forward and the exhaust manifold might be hitting the lower crossmember.
If it's a fan, just run your A/C at idle. When the compressor is on, the fans come on... look under the hood and you'll see/hear if a fan is hitting anything.