Unitary ambiguity of $NN$ contact interactions and the $3N$ force

We identify a redundancy between two- and three-nucleon contact interactions at the fourth and fifth orders of the chiral expansion, respectively. In particular, we show that tensor-type and spin-orbit three-nucleon contact interactions effectively account for that part of the two-nucleon interaction which depends on the total center-of-mass momentum and is unconstrained by relativity. This might give the chiral effective field theory enough flexibility to successfully address $A=3$ scattering observables already at N3LO.