You are getting your transmitted RF back into your radio that travels down the coax. It is a common problem with EFHW antennas. A common mode choke will help, but knowing where to put it can be complicated. The best place would probably be where the coax enters your shack (unless you have a ground radial wire at the antenna, in which case you can put the choke close to where you feed your EFHW. I like my EFHW, but it has been a bit of a battle, especially when using an amp.
Brett - K7TX