A derelict welcome mat on Terra Nova
A welcome mat
A welcome mat or doormat was a type of rug placed outside one's home typically with the word "welcome" written on it. In the cartoon Daffy Duck and the Dinosaur, Casper Caveman had a welcome mat outside his front door. (VOY: "Memorial")
A welcome mat was among the objects present at the abandoned colony on Terra Nova when it was explored by a landing party from Enterprise NX-01 in 2151. (ENT: "Terra Nova")
In an alternate 2263, Captain James T. Kirk commented about Jaylah's booby traps, referring to their use as a strange way to "lay out the welcome mat." Jaylah however, had no idea what a welcome mat was. (Star Trek Beyond)
In 2368, Commander William T. Riker characterized the increasing defenses around an artificial biosphere on Moab IV as being "not exactly a welcome mat.". (TNG: "The Masterpiece Society")
The term "doormat" could refer to someone who allowed others to take advantage of them. In 2370, Minister Jaro Essa likened the Bajoran people to doormats; they had been stepped on by any great power that happened by, such as the Cardassians and the United Federation of Planets. (DS9: "The Circle")