A nonsense verse referencing this pair of characters was to have been recited by Spock, while similarly under psychokinetic control (albeit by Charlie Evans instead of the Platonians), in TOS: "Charlie X". NBC even cleared the copyright of the verse, to allow for its usage in the episode. As written in the final draft script of "Charlie X", the verse would have been:
Tweedledum and Tweedledee
Agreed to have a battle:
For Tweedledum said Tweedledee
Had spoiled his nice new rattle.
In the final edit of "Charlie X", however, this verse was evidently replaced with one from "The Tyger".