‘Tell’ is correct as it is written Lobo.
I suspect you are thinking of ‘she tells’ or ‘the local gossip tells’, which is why you are confused, but ‘the local gossip’ is the object in this sentence, not the subject. Compare these:
She tells you / I’ll let her tell you…
They tell you / I’ll let them tell you…
He tells you / I’ll let him tell you…
The gossip tells you / I’ll let the gossip tell you…
The reason why I wrote ‘tell’ in my story is because ‘tell’ is the infinitive form of the verb dependent on ‘let’. This is the construction: Let someone do something. as in: Will you let me borrow your car? ‘Let’ has the sense of ‘allow’. You use the same construction with ‘allow’ except that this verb requires a preposition as in: She allows him to drive her car. This is exactly the same as: She lets him drive her car.