The regs about who is responsible are buried in the FCC Part 15 regs - governing unlicensed devices like TV sets and even the old kiddie low power 'walkie-talkies'.
If your radio is operating properly (and being operated properly) than it's generally the responsibility of the TV owner to fix his set.
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How about a few more details of your rig - power, band/frequencies, antenna. etc.
What TV channels are being interfered with ?
What sort of interference is it? Can he actually hear your voice or is it affecting the picture?
How about your TV ?
Has your neighbor told you the date & times of his being interfered with ?
Any other neighbors complaining ?
How far from your antenna to your neighbor's TV
Are you in a TV 'fringe reception' area ? IF so, then your neighbor may need a better outdoor antenna.
Does you neighbor have a TVI filter installed on his rabbit ears ?
Do both of you have AC line filters ('chokes') on your AC power cables to reduce 'common mode' interference. The snap-on ones that go on the power cord are usually adequate. I usually put on two or three and tape or shrink-wrap them to the cord.
Are you operating HF ? 6M ? 2M ? 220 or 440 ??
RF power ?
Your antenna ? What type, how high, aimable ?
Using an RF amp ?
Have you 'tuned' your antenna system ?
Do you use a tuner on HF ?
Do you have a low pass filter installed on your coax (only for HF) ??
And one of those 'dumb' questions: Does the TVI only occur while you are transmitting ??
Many TV owners blame all their reception problems on anyone nearby with a transmitter. It could just as well be his own baby monitor, furnace motor/oil burner, door bell transformer, or another nearby appliance or another neighbor's CB or amateur transmitter. Or it just could be that TV reception is lousy with the rabbit ears and his set is being overpowered with the emissions from your transmitter. Either way, he has to fix that.
Advice: Initially, until the source of the TVI is determined, do not offer to fix your neighbor's TV !