sorry, new flickr acct -- trying again to link the pix

Here is a link that might be useful: odd weed

It looks like dollarweed.

Here's a link:

Here is a link that might be useful: Dollarweed or pennywort

Yes, it is a Hydrocotyle species.
While the link above is interesting Hydrocotyle and this
species that is plaguing your mosses may not be a weed
species but rather a local native species.
In California, where I am at, there are three native species. It is a great plant for shallow water spots.
Your best course of action to contain it is to pull it up
when it gets started as it is viny in habitat forming
runners like strawberries which root out every now and then from whence a leaf grows.
I would recommend moving some of it into a small watertight bowl with some earth that sits just below the rim and flooding it until water sits on the surface and then plant in the Hydrocotyle and sit out in full sun or partial sun. An interesting accent for a table and fairly easy to contain as it is a shallow rooting plant.