When you use Pakt, the information of the pakts you make is stored on the blockchain and linked to the wallet you use. All the data on the blockchain is public so anyone can see it, but Pakt doesn't store any information that can be directly linked to your identity.
Custom pakts are validated by the person who made the pakt and are based on trust. They don't use any third party data.
For the other pakts such as the meditation pakt, you have to give the authorization to Pakt to read some fitness data from your Google account. Pakt uses this data to help you pick the right goal, and at the end of the challenge, to verify if it's a success. Pakt doesn't store anything on a private database.
The only information stored on the blockchain are the pakts you make and if you succeed. This information is linked to your crypto wallet and not to your real identity.