The algae itself isn't harmful. The only problem is that it may include certain types of algae or micro-organisms that you wouldn't want to introduce. For example, if it includes "hair algae" or blue-green algae, you'll be better off not introducing them, as they are especially obnoxious.
If you want to get rid of the algae, you I can soak them in a dilute bleach solution (one part bleach to ten parts water). If the ornaments are porous (like wood or porous stone materials), you then need to be super careful to remove all bleach, either by soaking in many changes of water + dechlorinator OR by letting the ornaments dry thoroughly (which probably takes a week or more, depending on how porous they are and how humid your house is).
Another approach would be to soak them in near-boiling water instead of bleach solution. Some materials will tolerate this, some won't.