The point is that the officials have said that you shouldn't have the word “if” there. Also, in my view, it doesn't make sense to have the “if” at the beginning of that phrase. It makes sense if you say.... I'll read it again. If you put it the way you're suggesting, it would read, “Those funds are to be used to compensate if the damage that is suffered occurs in the territory of a contracting state.”
That's not bad, but I think it would be better to say, “Those funds are to be used to compensate the damage that is suffered, if it occurs...”. I think that's a clearer wording.