Is this algae or a tiny seed?

Our pond was be clear, the first year.

Then, last year, it developed a green scum. It lasted all through the winter, and it’s still there.

Rick and I have been debating whether it’s some sort of seed, because they’re tiny, round balls, or algae. I say algae, but then we came across this plant and it sure looks suspicious.

Here is a pic of the seeds off of the plant.

Here are some pics of the crap itself: One

Two

Three

Our dogs go swimming in the pond, and they end up looking like this, yupid AND covered in scum.

If it’s algae, I’ve heard that barley hay can eliminate and prevent it. If it’s a seed from that plant, what can we do?