Translation:We have explained that we do not like pepper.
I think that both might be correct, and I think there was similar discussion about it somewhere.
Based on the Polish version, you are reporting on what you said in the past and is still true in the present. I believe in English some speakers will try to make the tenses agree, while others will analyze them individually (like Polish does).
I thought more about this. I think both work and there isn't a significant difference between them, though at first one implied something slightly different to me. I'm starting to think this is based on dialects. In mine, we just say what we actually said without changing the tense (maybe there are exceptions?). I would say, "I told him that I do not like Fallout 3," even though I do like it now. To me, it makes more sense to repeat what you actually said without changing the tense.