I have a filter for my well that backwashes into the sewer pipe. Since the hose cannot come in contact with the sewer, it sits above an open receptacle which has a trap beneath it and connects to the sewer pipe in the basement. About t feet further a clothes washer empties in the sewer pipe followed by the downstairs sink, tub and toilet about 8-12 feet away. This all empties into my septic tank. When I use the clothes washer, I can smell the sewer gases coming from the open receptacle for the filter backwash. Since there is a trap underneath this receptacle, I can't figure out how the gases are coming back into the house. What is causing this and how can I fix it?

First I would say that you need a plumber to check this out.But for general knowledge there are several possible reasons:1.Your outside vent stacks have an obstruction not allowing it to breath as the waste goes toward the septic tank.2.an obstruction in the main line before the vent stack in which case the vent stack was improperly installed(location and size) if this has always "done the dirty"
3.Sewage backup if on septic tank could also be the inability of the fill lines to take care of waste water.Pumping out a septic tank is only a temperary fix for a
Problem with the fill lines.Buy a sewer line snake or hire a plumber.The plumber knows exactly where to start. Snake before you let them dig!Ask for guarntee.

This problem began after I had the water filter installed. The entire septic system was recently replaced a few months ago and I thought this problem would go away but it has not. If anything, it seems to be worse. Is it possible that the drain from the clothes washer is siphening the water from the filter trap allowing the gases to escape?

cc I have a filter for my well that backwashes into the sewer pipe.
To began with you're putting a unnecessary load on your drainfield by discharging anything but sewage and gray water into the system.

Since there is a trap underneath this receptacle, I can't figure out how the gases are coming back into the house. What is causing this and how can I fix it?
A partial blockage cause that. Let me exp,ain. A major fixture, such as a washer discharges and then discharge hits a partial blockage and bounces back sending a bubble of sewer gas ahead of it. This bubble is what you smell. Snake and cle3an your sewer lines and if you can disconnect the backwash line and divert it somewhere else but back in your drainfield. Good luck, Tom