"His grandfather does not want to hear it."
Translation:Jeho dědeček to nechce slyšet.
You cannot not negate an infinitive like this. "On to nechce neslyšet" would be "He does not want not to hear it." the same way in Czech and in English.
What you do double-negate is words like no, nothing and similar:
"Nechce nic slyšet." "He does not want to hear anything."
"Nechce slyšet žádnou hudbu." "He does not want to hear any music."
The "main" verb in this sentence -- chtít -- is the one that is negative... he DOES NOT WANT to hear it. I don't think there's any reason to make the following infinitive (slyšět) negative. But I'm not an expert, so hopefully someone who is will give you a more authoritative answer!