When I clean my sump, I remove all the macroalge and leave it in RO/DI water for a few hours to cleanse it. I do it to ulva and red ogo, but same concept should apply to chaeto. They survive fine for a few hours in freshwater.
Believe it or not, cheato survives in freshwater nearly indefinitely... months and months ago, I ripped some out of my salt tank and didn't want to chuck it, so I made some baseball-sized clumps and put them in my 20gal fresh tank... they're still there, just as happy as day one.