It sounds like you are asking two different things.
Was Bruce Lee influenced by TKD? His close friendship with Jhoon Rhee would seem to bear this out.
TKD's influence on JKD is less clear. Bruce was investigating many arts that use kicks - including Tang Soo Do, Muay Thai, Savate - not to mention the Northern Kung Fu styles that he was already familiar with.
I would say that modern JKD kicking tends to be built primarily off of either Muay Thai or Savate.
"In case you ever wondered what it's like to be knocked out, it's like waking up from a nightmare only to discover it wasn't a dream." -Forrest Griffin