Is the Relay dropping out?
This normally doesn't happen but when you have that type of noise presence - can't help but wonder if your relay is clicking - as it - it wants to drop out.
Otherwise - the "ALC" sense circuit "sense" trace arrives to FET5 from the back of the board between 2 coils L29 and L28 - - but it does thru a capacitor to keep the "live" signal current (DC Block) and lets the RF pass - but it goes thru a divider set up with a "variable" and a fixed value - and to keep DC off of it, so the FET doesn't blow up - a simple coil to act as that "shunt" across to ground - then onto a Diode and 10K resistor then the FET itself (simpler 0.047uF smoothing cap is located here)
The FET - if these radios been in storage after a storm of has been left connected after a couple of close lightning strikes - the FET itself can turn into a "transistor" (Fused pellet junction) and might need to be replaced.
The Diode and resistor are a type of constriction valve - looking for Negative peaks to act quickly with, but the 10K also with the Diodes one-way valve action - allows positive peaks to be sensed as well.
So, what this tells me the FET may be damaged or shot - the junction is too sensitive now and although a simple SK192 would work - the whole circuit needs a good going over in parts and even the diode itself - might need replacement.
But to answer that, the whole mess should get "pulled" off or disabled to verify that the ALC is causing this.
The issue of the relay becomes more paramount when the relay contacts are not perfectly clean and "bounce" or have a resistive element in them. This generates an SWR bump that blows up the Final in this scenario - so if the Relay has suffered damage or you don't know it's condition - then no matter what you do to fix the "click" the relay may be the whole problem.