When you connect your iPad to a projector you should only see the fullscreen content area in the projection, without the user interface.
Unless you enable “Demo Mode” (in Main Menu > Settings > Advanced > External Display > Demo Mode) - this setting causes the user interface to be shown in the projection too, along with visualizing your touches as blue circles. This is meant to be a way of teaching Tagtool, for example in a workshop.
If Demo Mode is set to off, you should only see the content.
If the problem persists, please let us know which iPad model and iOS version you are using!