TypeApp supports integration for .ics type invites by allowing you to add events to your local calendar application:

We are working on a major release to TypeApp that we are truly excited about (version 2.0). Once we release it, we will support full calendar background sync as well as other features.

Currently, we support integration for .ICS type invites by allowing you to add events to your local calendar application. Please tap on this attachment and open with your calendar.

invitation_add_to_calendar