Translation:They were saying that they do not like strawberries.
Sequence of tenses always utterly confuses me. Maybe it is possible, but to make it more clear I just changed the default sentence to "that they do not like strawberries". That's still correct and seems to make more sense because liking something is more general and usually not dependent on the time.
I guess that is what people seem to be saying in English now, or at least that is what one sees on Duolingo programs. I must admit that the sequence of tenses I usually use would insist on "that they did not like strawberries," as I think you originally had. I think we may be seeing English moving from the sequence of tenses used in Romance and most Germanic languages to the one used in most Slavic languages, in which the tense of the reported speech is not changed at all.