How do I get rid of the piggy bank?

It will go away/expire once it is full (you will get the diamonds from the Primary and Special Ops missions only) and you decide not to buy it - usually about a day after it has been filled to the maximum amount, depending which level/city you are playing.

At the end of the expiry time, it will ask whether you want to lose the diamonds - you will only get to keep them if you are willing to pay the amount listed (and be careful if you are going to pay, as sometimes you may go to buy the diamonds at the price they put on the screen, but the amount they are going to charge you once it goes to the payment screen is higher).