Fortunately for the show (and lovers of “Soft Kitty”), the lawsuit was dismissed by a judge in 2017, and “Soft Kitty” can continue on both The Big Bang Theory and Young Sheldon.
Interestingly, there was once a time when it wasn’t guaranteed that The Big Bang Theory could continue to use “Soft Kitty,” let alone pass it over to Young Sheldon.
Back in 2015, the daughters of the poet who wrote the original rhyme on which “Soft Kitty” is based filed a lawsuit, intending to claim a share of the show’s profits and prohibit Big Bang from ever using the song again.