Why a system of three bosons on separate lines can not exhibit the confinement induced Efimov effect

We study a system of three bosons interacting with short–range potentials which can move along three different lines. Two of these lines are parallel to each other within one plane. The third line is constrained to a plane perpendicular to the first one. Recently it was predicted in physics literature [NE17] that such a system exhibits the so–called confinement induced Efimov effect. We prove that this prediction is not correct by showing that this system has at most finitely many bound–states.