In pure superfluid 3He–B at ultra-low temperatures, the quartz tuning fork oscillator response is expected to saturate when the dissipation caused by the superfluid medium becomes substantially smaller than the internal dissipation of the oscillator. However, even with a small amount of 4He covering the surfaces, we have observed saturation already at significantly higher temperatures than anticipated, where we have other indicators to prove that the 3He liquid is still cooling. We found that this anomalous behavior has a rather strong pressure dependence, and it practically disappears above the crystallization pressure of 4He. We also observed a maximum in the fork resonance frequency at temperatures where the transition in quasiparticle flow from the hydrodynamic to the ballistic regime is expected. We suggest that such anomalous features derive from the superfluid 4He film on the oscillator surface