Backfiring happens though the exhaust OR intake. In most cases, it's the exhaust, on an engine like this, with a "lost spark" design. Each turn of the flywheel energizes the coil and fires the plug, both on compression and exhaust strokes. If the mixture is too rich, excess fuel can ignite on the exhaust stroke.
Too rich mixture can happen when the air supply is restricted:
a. engine was tipped over the wrong way and air filter is clogged with oil.
b. air filter is clogged with dirt/debris
c. choke not working properly, sticking open when it should close.
Since the mower was not backfiring before you took it in, I'd be on the dealer to make it right, especially since you are still under warranty. Might want to quiz the dealer and see what they say. Give the dealer a chance to make it right. If, like Mr. Jagger said if (you) "can't get no...satisfaction" for sure contact Honda Customer Relations at 770-497-6400. Have your mower's serial number, dealer info, etc. when you call.