This was supposed to have been corrected ONE YEAR AGO, but the error still persists!
Not sure if you mean that there should be an -e to léché?
In fact, no -e is required because in this case
se lécher la patte
just as in
se browser les dents
if the direct object 'la patte' or 'les dents' is after the verb, there is no agreement of the past participle.
So the example in the lesson is correct.
Pourqoi ma chatte s'est-elle léché la patte?
Yes, this can be a bit confusing, since you learn that you always agree the participle in reflexive clauses. However, this is not the proper way to phrase the rule. The rule is that the participle agrees with the COD if the COD precedes the participle.
Ils se sont levés tôt hier.Nous nous sommes rejoints devant le cinéma.Elle s'est brossé les dents.Ma chatte s'est léché la patte.
Notice how in the first two sentences the COD is identical with the reflexive pronoun and appears before the participle. Therefore, the participle is made to agree in these two cases.
In the last to example, the COD is different from the reflexive pronoun and occurs after the participle -- hence, no agreement.
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