Rob,
It is easy to open up and clean the the check valve(s). The cutout on the front side of the valve bank has three check valves in a row between the hose in/out bank.
First figure out which of the check valves you want to clean by tracing the hoses back to the valve.
Then prop the front arms on something solid and bleed off the pressure by cycling the valves. (Trust me you want to do this.)
Then get it really clean, (Terry's comment about open heart surgery clean applies.) and unscrew the nut between the hoses. Under the nut is a check valve assembly. Mine had a spring in it, but it is a simple plastic piece.
Oil will leak out even if you relieved the pressure.
Clean the check valve and the valve seat, and the surrounding threads and area. Reassemble.
It isn't too hard, just remember that you are disassembling this because it has a small piece of gunk in there, so you don't want to trade one piece of dirt for four new ones.
Again, I would like to stress the importance of having the front arms resting on something solid that will support their weight while you are underneath.
All the best,
Peter