Should I install a hot water recirculating pump before or after the thermostatic mixing valve?
I believe that Grundfos comfort system is comprised of two parts:


The Pump
A special tee fitting


The pump is installed on the outlet of the hot water tank and the special tee fitting is installed on the furthest fixture in the house from the hot water tank. This special fitting bridges the hot and cold water supplies. The basic concept is that when the hot line is not in use, it will cool off. This special tee fitting allows the pump to pull the cooled off water in the hot water line back to the tank through the cold water line. This reduces the amount of wasted water that is poured down drain while waiting for hot water.

In your case, you are going to want to install the pump on the outlet (common port) of the mixing valve. This will allow for the proper loop to be created as well as to maintain the proper pressures on the valve as noted by UNECS.

As for advise on cutting the existing out, you're going to have to remove the entire portion from the wall back to the mixing valve outlet. It also looks like there is not enough room left on the pipe sicking out of the mixing valve to reconnect a new fitting to. You may have to sweat out the pipe and solder in a new piece, but be careful not to overheat the mixing valve as you will damage the internals. If you are going to be soldering the new pipework, keep in mind that the existing fittings that have been used are ProPress fittings which have a rubber seal inside of them (the bump in the hub) and that you need to be careful not to overheat them as well. In both cases you can wrap the fitting or valve with a wet cloth to help keep them cool.