Because you use an off-the-shelf item there is no much you can do to modify it ..
In other circumstances I would encourage you to build your own “power controller” based on two back-to-back SCRs (to avoid problems that you have with this most likely triac-based controller) ..
However, you can try to connect LC filter, consisting of an inductor (at least 1mH) and >220nF (@250Vac) capacitor, between the output of your black box and the load ..
First, using an ohm-meter identify which connection loops-through the black box from input to output, then install inductor on the other output wire, and the cap in parallel with the load .. see picture below ..
Rgds,
IanP