I have a 2005 37PC. Yes, you have to access the pump to clean out the filter on the inlet side of the pump. Unfortunately, you do have to remove the refrigerator to get to the pump. The way I removed my refrigerator was to remove the outer cabinet door. To remove the outer cabinet door you need to take off the lever that some installations have that attaches the outer cabinet door to the refrigerator. On the hinge side of the cabinet door there is a there is a piece of wood painted black mounted vertically toward the aft of the boat that is screwed into the forward wall of the head. (it will become obvious when you start to look at it) Remove the screws for that piece of wood with the hinges attached and the outer door will be able to be removed. You may have to work it out a little bit by pushing the carpet down as you pull the bottom of the wood out. Once you have that done you should be able to get to all the mounting screws that hold the refrigerator in. Once you remove those screws (maybe 6 or 8) you will be able to pull the refrigerator out. I would suggest putting a big towel or blanket under the refrigerator or it may tear the carpet or scratch the flooring. Once you have the refrigerator out you will be able to see the pump. On the forward side of the pump you will see where the cold water supply from the tank connects to the pump. Take the supply line off and that is where the filter is located. (to get the supply line off push the line in and there is an inner ring that also pushes and then pull the supply line out once again it will become obvious when you get in there) All you have to do is remove the filter assembly from the pump and you find the screen in there. Clean the filter and put the assembly back together.
Now you just take a little break.
So that I never had to go through this process again I installed and inline filter on the cold water supply from the tank that I could easily access by removing the trash container or the cabinet under the sink. This has proven to be a life saver. I have attached a picture below any good marine supply store will have one. When you install it make sure the screen is up. You simply unscrew the clear plastic top and remove the screen clean it and put it back together. I make sure to have a small towel under the assembly to collect the water that come from the assembly.
I almost forgot don't forget to install a shutoff valve prior to the inline filter otherwise the water from the tank will run out making a mess. Picture below.
Make sure to check for leaks before you put the refrigerator back into place.
I am exhausted. Good Luck
Joe