Nobody likes to pay for something they've already bought.
The license check contacts Google to make sure your purchase has gone through and is applied to your account. If this check fail for some reason, please check and confirm the following:
1. Make sure that you are logged in to Google Play using the same Google account as the one used at the time of the app purchase.
2. The license check requires an internet connection in order to contact Google. Check to see that your device is connected to the internet. Sometimes WiFi can be unstable so if you can, we'd recommend mobile cellular networks.
3. Did your purchase really go through with Google? You can see your previous purchases by logging into you Google Wallet and clicking on the ReadMe! order. Make sure that it say something similar to "Status: Complete".
4. According to Google, some users might receive a license check failure after making the switch from @googlemail to @gmail. This can be fixed by clearing their Google Play store data (Menu > Settings > Applications > Manage applications > All > Play Store > Clear data).
If you've gone through and verified the checks above and it still doesn't work we would be more than happy to help you out. Get in touch with us and tell us the ReadMe! order's Transaction ID (looks similar to XXXXXXXXXXXX.token.XXXXXXXX)