Thank you for not wanting to hurt the cat. It is probably upset by your cat who is loved and cared for.
Cats do hold grudges and never let them go! This is not an easy problem - there are sprays available such as "Tom-Off" or "Boundary" which are usually used to defend females from males during mating times. These sprays work well in warding off unfriendly advances.
Alternatively, you could try to get them to make peace with each other. Show both loving attention and offer the interloper strokes, tickles and cat biscuits when you feed your cat.
You could also try to seal up your house for a while - until the other cat forgets his grudge or just gives up. Speaking to the cat owner might help too - they may not know what their cat is up to.
Make sure it is not your cat causing the problem - if your cat is antagonising the other one, try to break the habit.