Te purpose of the gas filter is to keep foreign particles and oil from the rest of the gas components. Not all refrigerators have a filter. In fact, all the new models don't.
The filter is simply a gas fitting with a gauze-like material inside that traps any foreign particles. In theory, this seems like a good idea, but in reality filters are never easy to change (and seldom available) and can eventually create their own problems.
Troubleshooting. There are two common problems associated with the gas filter. An obvious problem with the filter is when nothing passes through it. It's plugged. Another, more subtle situation, is when some gas passes through it, but not enough gas passes through it. A good indication that this is happening can be demonstrated when lighting the burner. If when you light the burner, the flame is at first vibrant and then, within a matter of seconds, it drops to something not as healthy looking, this is a sign of a partially clogged filter. What happens is that when the burner is off, enough gas has passed through the filter to fill the other components with propane at the correct pressure. When the flame is lit and gas begins to flow, not enough gas is allowed to pass through the filter to keep up with the volume and the pressure drops.
If it's determined that the filter is a problem and you can get a new one, always replace it. If you can't get a new one, then you'll have to consider gutting the old one. To do this, remove the filter from the system and then remove everything from inside the filter. Be absolutely sure that you have removed everything from inside the filter before reassembling. If you don't, what's left inside the filter will become a foreign particle in some other component down the line. This could create a serious problem like preventing the safety valve from closing completely.