There's apparently a small value of capacitive coupling letting the fast transitions appear.
Estimating the capacitance may give you a few hints for troubleshooting.
It could be a broken connection at the BNC, defective relay, or fault somewhere in the low frequency path in the front-end.
Even without schematic comparative probing should get you to the problem easily, the main issue is how to run it disassembled while keeping things cool.