I like string algae so I leave it unless it does something like filling in the upper little pool where the birds bathe. I love watching it flow in the stream and in the pond. I have heard, but don't know if it's true, that if you have string algae you won't have free floating "pea soup" type of algae. Anyway, unless it is causing a problem, I let it be. I think it is "to each his own" when it comes to string algae.

I don't actually mind it in the pond, but am a bit concerned with covering the roots of the hyacinths (I'm finding it's making the roots float on the surface rather than down into the water the way they normally do). I'm considering taking them out and leaving them overnight in a container with some algaecide, then wash the roots off good before sticking them back into the pond.

CaraRise,
Don't use algaecide.
Use Hydrogen Peroxide.
Lightly, over the string algea on the roots.
Itll kill the algea, but not the plant roots.
Then you can just put them right back in the pond.

Consider adding more water lilies. Cover 60% of the waters surface with water lilies and the string algae will die back as the water lilies get bigger. This will work well. Or try adding more oxygen producing plants. You need more plants. Algae fights for the same nutrients and with enough plants the algae will not grow and your water will be clear and clean.

Here is a link that might be useful: Gabelmans Gardens blog

The water hyacinths alone cover 60% of the surface right now. I have three dwarf water lilies. I don't think a pond my size can support more.