tug at somebody's heartstrings

tear/tug/pull at/on (one's)/the heartstrings

To elicit strong feelings of sympathy or fondness. I don't know why, but that piece of music always tears at my heartstrings. That documentary really pulls on the heartstrings—you'll want to adopt all of those kids after watching it.
See also: heartstring, on, pull, tear, tug
Farlex Dictionary of Idioms.

tug at somebody’s ˈheartstrings

make somebody feel strong emotions of sadness and pity: Advertisers often use babies and children to tug at your heartstrings.
See also: heartstring, tug
Farlex Partner Idioms Dictionary
See also:
  • tear/tug/pull at/on (one's)/the heartstrings
  • tug at the heartstrings
  • heartstring
  • play on heartstrings
  • play on the/(one's) heartstrings
  • strike a chord
  • strike a chord (with someone)
  • strike/touch a chord
  • touch a chord (with someone)
  • play with