No, not as a thank-you for paying your taxes. It’s some sort of save-the-trees promotion by Starbucks:

Join the movement. On April 15th, bring a reusable travel mug into your local Starbucks and get a free brewed coffee.
One person can save trees, together we can save forests.
For the good of the planet, Starbucks is encouraging everyone to switch from paper cups to reusable travel mugs. One day in March thousands of New Yorkers made the switch. Join them now by taking a pledge to do the same.

Do you know what might really save the planet? How about taking the pledge to no longer buy coffee at a store and only drink what you brew at home?