A method for dynamically filtering a wash mixture of a washing machine can include providing a textile to the washing machine and washing the textile therein during a washing operation of the washing machine to separate a plurality of contaminants from the textile, such that, upon separation of the plurality of contaminants from the textile, the plurality of contaminants are received in the wash mixture to form a contaminated wash mixture. The method further can include extracting at least part of the contaminated wash mixture to an extraction system in communication with the washing machine, as well as filtering the at least part of the contaminated wash mixture in at least one filtration stage of the extraction system to attract at least one metallic or magnetic contaminant of the plurality of contaminants using at least one magnet.