Reducing the carbon footprint isn't enough. The problem with limiting the efforts of preventing global warming to trying to reduce the emission is that there are those who don't care. You can also only get your footprint down to zero anyway. It's also inherently a negative term, something you need to stop producing or at least try to minimize.
In this world we need more positive attitude. Words and terms can affect things a lot. It's also easier to get into the growth mindset when there is something that is good when it actually grows. Making a positive impact feels more meaningful.
Ecological handprint is the odea that your actions can have that positive impact. It's something concrete you do to add something good to the world instead of just trying to fight back and reduce. Leaving your handprints in the world is active and doesn't feel like a sacrifice.
Even if the handprint you leave is the actions you do to reduce your carbon footprint that already sounds better. But with this active approach it is also easier to influencing others and start working towards something bigger and better.