  We investigate the importance of the three-nucleon (3N) force contact terms
in elastic nucleon-deuteron (Nd) scattering by applying the N$^4$LO$^+$ chiral
semi-local momentum space (SMS) regularized nucleon-nucleon (NN) chiral
potential supplemented by N$^2$LO and all subleading N$^4$LO three-nucleon
force (3NF) contact terms. Strength parameters of the contact terms were
obtained by least squares fitting of theoretical predictions to cross section
and analyzing powers data at three energies of the impinging nucleon. Although
the N$^3$LO contributions to the 3N force were completely neglected, the
results calculated with the contact terms multiplied by the fitted strength
parameters yield an improved description of the elastic Nd scattering
observables in a wide range of incoming nucleon energies below the pion
production threshold.
