If the App is requesting that you make a purchase the you have already created either 6 clients or visits. You can only have up to 6 clients and or visits on the free app. If you purchase the unlimited option then you will be able to create as many clients and visits as you like.
You can delete a visit by selecting the visit you want to delete and pressing the X button bottom right of the client visit page. If your client only has one visit then you will get a popup asking if you want to delete that client. If you confirm then you will delete that client from memory.