It just so happens I am a Customer Service Lead and Manager on Duty at Staples #1275 in Massachusetts, so let me explain the process to you.
This week we're having our HP Ink promotion. The way it works, is that you pay $59 dollars or more in HP Ink and if you recycle ink cartridges in the same transaction (up to 10 a month for regular Rewards Card Members, or 20 a month for Premium Members) you receive $5 a piece back on your monthly ink rewards check in place of the usual $2
As long as your rewards number is showing at the top of the receipt you will receive your money back in the form of a staples rewards check either in your e-mail or delivered to your home at the end of next month.
If you're not sure how you normally receive your rewards check, you can go to http://www.staplesrewards.com and register an online account. This will also give you access to viewing your transactions and printing out available rewards checks; you can even update your personal information.
So to make a long story short, you should receive your money in just about a months time. Good things come to those who wait!