I have the same problem. After considerable research, including discussions with several manufacturers (who were not always of the same mind) I think I now have an understanding of the problem. Understanding ad applying a solution is another issue.
Electric baseboard heaters use room air. Thay are quite simple. Metal plates are heated and thus heat the room air by convection. Room air is pulled in at the bottom, heated by convection and released through the top vents. The warmed air is attracted to cool surfaces. Because the heater is generally flush with an exterior wall surface, the heated air is immediately attracted to the cool wall behind the heater. Any dust in floor carpet or that has settled on the floor is carbonized in the haeting process and adheres to the cool wall as it rises with the warmed air. This the asme process that transports air pollutants thousands of miles in the atmosphere. This problem is particularly noticeable if there are sources of contaminants in or near the room, i.e. smokers in the house or if candles are burned. There are several things that can be done to help.
The first consideration is replacement. After years of heating and cooling metals in the heater fins do start to break apart. This is not a major part of the proble, but consideration of the systematic replacement of 20+ year old electric baseboard heaters is not unreasonable. I have replaced some heaters, but when doing so I have also reset the heater farther away from the wall by extending the wood baseboard behind them. I have noticed that the new repositioned heaters are cleaner. Where I have replaced heaters away from the wall I have noticed a difference. In addition, however, keeping them and the room clean with minimal dust is imperative. I have also placed a high performnace room air cleaner in those renovated rooms. Im sure that has also helped.
One question that I have not been able to answer is whether replacing heaters with the newer, soposed more efficient, liquid filed electric baseboard heaters would be cleaner. I am also interested in any feedback on the efficeincy of those heaters relative to conventional baseboard heaters.