What’s a better way to design this form?

This is by Doodle, a neat little service for coordination of meetings (no affiliation etc.). Once an invitation is sent out to participants, they get this form.

What, um, ticks me about it is the part I marked. enter image description here

Specifically, I see two issues with it:

  1. They changed the functionality of what's probably the single most standard control in the world - a regular checkbox.
  2. They notify the users of this change in a way that doesn't seem to be very elegant or efficient.

What would be a better way to solve this form?