How do we unclog the overspill filter/drain in refrigerator?

Our refrigerator is leaking water, drown from the freezer into the lower part of fridge. Refrigerator is working fine (freezer too) but the filter that takes the water from the freezer appears clogged, how do we unclog? The cup is at an odd angle (very close to the top of the refrigerator). Is there something we can put into it, that will not ruin our refrigerator?? Moffat refrigerator, only about 6 years old, frost free, upper freezer (with door).