Translation:I have a strawberry that is redder than that one.
Este, esto, esta are terms used for 'this'.
Ese, eso, esa are terms used for 'that'.
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The article before 'strawberry' needs to be 'a' not 'the'. Be careful to keep them consist when moving their position in the sentence. You made it to mean only one strawberry is in possession rather than out of the multiple strawberries 'I have' one is redder than that [one].
This "ésa" is a pronoun - "... more red than that [one]." The accent mark may not be necessary, but it is not wrong, and in fact it helps to distinguish intent.
Duolingo is wrong here. Their record with accentuating demonstrative pronouns is spotty at best. Sometimes, as here, they chide you for accenting letters where it's right; other times, they say the accent is required. They need to clean up their act.
Que can mean that, but here it is part of a phrase. Like tan grande que (as big as) or mas azul que (bluer than/ more blue than. Personally I would say more red in English if the other strawberries had green or white tips marking them as not yet ripe, and redder if I was referring to the shade of red being brighter and darker vs. An orange-red.