¡Hola Fg109 y ricardo-rich!
Ricardo, you are on the right track. This is a slightly tricky area, though, because it's one of those instances where we have what is grammatically correct on the one hand, and what people actually say on the other.
Let's start with how this works grammatically in Spanish. The word gente "people" in Spanish is a collective noun, just like the words "team" or "group" in English. In North American English, collective nouns are always singular - for example, the sentence would be "Our team was great!" and not "Our team were great!" - and in Spanish, it's the exact same. That's why we say la gente es and not "las gente son."
So, why do you sometimes see and hear sentences like Mucha gente (singluar) te va a hablar sin importarles (plural) tu gramática in Spanish? The answer is that although this isn't strictly correct, it is how some people talk. You may well hear a number of native Spanish speakers use les when referring to the collective noun gente, because they're thinking of this noun as a plural. To be grammatically correct, this sentence should actually read Mucha gente te va a hablar sin importarle tu gramática.
This is also likely a bit of a joke here, because the speaker explains how people won't care about your grammar, and he makes a common grammar mistake while doing so.
This sentence definitely gives the wrong impression, though. I will pass this on to our course development and audio teams and see that it gets taken out of the lesson.
Our apologies for the confusion! I hope that this explanation was still useful.