Polarized small-angle neutron scattering was used for studying of critical fluctuations in the Dzyaloshinskii-Moriya helimagnets Mn$_{1-x}$Fe$_x$Si with $x$ = 0.10, 0.15, 0.20. The Mn$_{1-x}$Fe$_x$Si compounds are helically ordered below $T_c$ and show a helical fluctuation regime above $T_c$ in a wide range up to $T_{DM}$. The critical temperatures $T_c$ and $T_{DM}$ decrease with $x$ and tend to 0 at $x = 0.11$ and 0.17, respectively. It was shown experimentally that three samples reveal properties of fluctuations in different regimes. The sample with $x$=0.10 provides sharp narrow peak in polarized SANS maps for temperatures near $T_c$ and in the ordered phase, whereas in the one with $x$=0.15 critical fluctuations are suppressed by the disorder which destroys long-range magnetic order, corresponding scattering peaks being substantially wider than for $x$=0.10. For the sample with $x$=0.20 even at lowest temperatures only traces of the half-moon scattering patterns are visible. The degree of the scattering polarization is close to 1 for all three samples meaning that the corresponding helical fluctuations are chiral. The Mn$_{1-x}$Fe$_x$Si compounds represent an example of the system where ferromagnetic exchange approaches zero but Dzyaloshinskii-Moriya interaction is finite and provides chiral rotation of spins in magnetic fluctuations. We argue at the qualitative level that observed peculiarities can be attributed to defect antiferromagnetic bonds which are added to the system by Fe ions and lead to finite correlation length of the spiral at small temperatures for $x>x_{c}$.