ML,
I've never had Chara rise to the surface. Typical algae yes. If you can get it out I would remove it.
I just raked out most of the Chara from my trout pond. I have blisters on my hands to prove it. I would have gone inside to get the gloves but I was afraid I would be tempted stop and not complete the job.
And you know I just raked it out a month and a half ago!