There are two issues that trigger backfire on a K75.
One is the gasket between the header and the muffler. The leakage of air into the exhaust tends to ignite unburned gasoline within the exhaust system. That is often throughout deceleration. You possibly can typically visually see if the the gasket is dangerous. It’s a sleeve that goes over the header and contained in the muffler. Clearly, a leak earlier than the muffler could cause fumes. Ive changed many of those on different peoples bikes, particularly if they’ve eliminated the muffler a time or two. They get broken VERY simply throughout that process.
The opposite explanation for backfire (however often not fumes) is a misadjusted throttle place swap. It tells the pc to cease injecting gasoline if the RPMS are above 1800 RPM AND the throttle is totally closed. This causes backfire due to all the surplus unburned gasoline that will get into the exhaust.
Clearly a very long time BMW proprietor. Thinks $16 is dear upkeep.