From my understanding, me as a clitic is reserved for tonic clitics (stressed). And as indirect pronoun, in this instance shouldn't we use mi instead?
PS: this is one of the translation question from Duolingo.
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Mi, ti, si, ci and vi, if followed by the pronoun ne, become me, te, se, ce, ve. The same happens if they are followed by lo, la, li, le.
Me lo ha detto lui (Lui mi ha detto una cosa)
Te la ha data lei, questa notizia (Ti ha dato lei questa notizia); “Te l'ha data” is the same as “te la ha data”.
When followed by a direct object pronoun, the pronouns mi, ti, ci, vi and si are replaced with me, te, ce, ve and se, respectively.
The same rule applies to gli, but together with the direct pronoun it must be replaced with a contracted form:
gli + lo => glielo, gli + la => gliela, etc...
You can find a better and more thorough explanation here