The users can request contact data change in a special form and their requests must be approved by an administrator by default.
However, you can automatize this process and let submitted changes be projected to signatures automatically in Settings - if you trust your users, this can significantly lower your workload, especially in combination with Subscription.
Unless you configure this in SignatureSatori, users won't able to edit their signature in the app directly, BUT they still can change or edit the signature in their e-mail client.
If you want to prevent users from doing that, we advise you to choose Subscription mode - all signatures are updated daily and set to their desired state.