A customer reports that the Invoice ID, rather than the Invoice Number is passed along to Stripe. This number is then included on client's credit card statements. It's possible that this issue exists in the official Stripe gateway as well, but I thought I would mention it here in case @Cherry doesn't mind taking a peek.
We have released version 1.0.2 of this gateway today, which patches a small bug that prevented users from making "credit payments", and depositing funds not applicable to any invoice. We also took the opportunity to update the Stripe PHP SDK version, which patches a few issues. Full changelog: https://github.com/nodecraft/stripe_plus_gateway/blob/master/CHANGELOG.md
Download the latest version at https://github.com/nodecraft/stripe_plus_gateway/releases
The API deals with CRUD actions on data. A page is not data in this respect, and is not available via the API.
You'll want to either create your own pages using the data you retrieve via the API, or link to a Blesta order form, for instance, to have customers checkout.