Uranium and thorium in heavy rocks have a decay chain which includes a three-day isotope of radon. If a building has materials with some chemically-insignificant mixture of uranium and thorium, such as concrete or granite, then the radon can diffuse out of the material into the air. This is part of your normal background radiation, unless you have accidentally built a concrete basement with granite countertops and poor air exchange with the outdoors, in which case the radon can accumulate.
When radon does decay, the decays leave behind ionized atoms of the heavy metals polonium, lead, and bismuth. These ions neutralize by reacting with the air. Here my chemistry is weak, but my assumption is that they are most likely to oxide, and I assume further that the oxide molecules are electrically polarized, like the water molecule (the stable oxide of hydrogen) is polarized.
Polarized or polarizable objects are attracted to strong electric fields, even when the polarized object is electrically neutral. Imagine a static electric field around a positive charge. A dipole nearby will feel a torque until its negative end points towards the static positive charge. But because the field gets weaker away from the static charge, there’s now more attractive force on the negative end of the dipole than there is repulsive force on the positive end, so the dipole accelerates towards the stronger field. If you used to have a cathode-ray television, you may remember the way the positively-charged screen would attract dust much more than other nearby surfaces.
Clothes dryers are very effective at making statically charged surfaces. (Dryer sheets help.) So when radon and its temporary decay products are blown through the dryer, electrically-polarized molecules tend to be attracted to the charged surfaces. The decay chain is
If your Geiger counter is actually detecting radiation, it's almost certainly the half-hour lead and bismuth. Constructing a decay curve would make a neat home experiment (but challenging given what you've told us here).
True story: I was once prevented from leaving a neutron-science facility at Los Alamos after the seat of my pants set off a radiation alarm on exit. This was odd because the neutron beam had been off for weeks. It was a Saturday, so the radiation safety technician on call didn't arrive for half an hour — at which point I was clean, so the detective questions began. I had spent the day sitting on a plastic step stool. The tech looked at it, said that radon's decay products are concentrated by static electricity, and told me that I needed to get a real chair.