The idea is to engineer a suitable species of filter feeders like clams, mussels, crustaceans, which would then filter river water and accumulate a very specific rare-earth element. Periodically the animals would be harvested and the rare element extracted.
Alternatively, the same could be done in the sea. Nets containing engineered filter feeders could be dragged along the areas known to contain a specific rare element. Such nets could be dragged by cargo vessels. This would result in higher energy usage as compared to river filtering.
This idea was inspired by Juran's idea to mine heavy metals by filter feeders.