Removing and bypassing the board with the coils on it would be a good start. The marking "LPF" means that it's a low-pass filter, meant to reduce interference caused by harmonic frequencies coming out of the amplifier.
Just one problem. The parts on it are too small, and that board is famous for flaming out.
While you're at it, replacing the coax that runs from the load control to the relay will now be necessary if it won't reach the whole way to the relay.
The new coax really needs to have the shield grounded. Preferably at both ends. The factory coax is always installed with the shield not connected to anything.
At all. This is a bad idea and causes feedback problems.
If the old coax will reach to the lug on the relay, you can strip a quarter inch of the jacket from each end of the coax, wrap a piece of hookup wire around the exposed braid and (gently) solder it to the braid. Make the ground connection to the other end of the hookup wire, keeping it as short as you can.
And if it won't reach the lug on the relay, you need a new piece of coax. Just don't use one with foam dielectric. It won't hold up to heat. Foam will soften and eventually allow the center wire to short to the braid.
73