It's a waste of time remembering those who don't remember us.
"those" is plural, so it requires the plural "do" rather than "does" (don't vs doesn't). Replace "those" with "they" and you will perhaps hear it better ... they don't remember (not they doesn't remember).
"People" is also plural, and redundant. You can leave it in the sentence if you wish (to distinguish from dogs, perhaps?) but unless you need that distinction, we can assume you are speaking of people.
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