The bowtie can be worn by most Omega-Kerfur via the "equip" option. This option will display on Omega-Kerfur while hovering over it with any valid equipment in the player's hand.
To get the bowtie back either use the "unequip" option while hovering over an Omega-Kerfur that has it equipped, or deactivate it via any means to have the bowtie drop.
Obtaining
Two bowties can be found on top of some supply boxes in the tree polygon test area.
Gallery
Bowties on a supply box in the tree polygon test area.
An Omega-Kerfur wearing a bowtie.
Trivia
The "Keljoy" Omega-Kerfur model has a bowtie always equipped.