Nibbles, 6.5 5.5 bytes (11 nibbles)

|$>2`'=~$$

|$              # filter each word int the input by
      =~$       #   group the letters by
         $      #     themselves,
    `'          #   transpose this list of lists,
  >2            #   and remove the first 2 elements
                #   (so if there is at least one letter
                #   present >2 times, the resulting 
                #   list will have nonzero length)

Nibbles, 6.5 5.5 bytes (11 nibbles)

Edit: -2 bytes by using transpose, inspired by Jonathan Allan's Jelly answer

|$>2`'=~$$

|$              # filter each word int the input by
      =~$       #   group the letters by
         $      #     themselves,
    `'          #   transpose this list of lists,
  >2            #   and remove the first 2 elements
                #   (so if there is at least one letter
                #   present >2 times, the resulting 
                #   list will have nonzero length)

Nibbles, 6.5 bytes (13 nibbles)

|$/.=~$$>2$:

|$/.=~$$>2$:
|$              # filter each word int the input by
    =~$         #   group the letters by
       $        #   themselves
   .            #   and for each group   
        >2      #     remove the first 2 elements
  /             #   now fold over all groups
          :     #     appending them together
                #   (so if there is at least one letter
                #   present >2 times, the resulting 
                #   group will have nonzero length)

Nibbles, 6.5 5.5 bytes (11 nibbles)

|$>2`'=~$$

|$              # filter each word int the input by
      =~$       #   group the letters by
         $      #     themselves,
    `'          #   transpose this list of lists,
  >2            #   and remove the first 2 elements
                #   (so if there is at least one letter
                #   present >2 times, the resulting 
                #   list will have nonzero length)