For reproducibility reasons (how users are prompted is part of a study protocol, which ideally is also submitted as part of ethical approval, etc.), it is currently originally locked in. Correctly instructing the user of these consequences is a UI concern.
But, for flexibility reasons (not all studies have equally strict requirements), I did think ahead and didn't want to prevent changing invitations entirely. In short, it's a restriction in the current studies subsystem, but not in the deployments subsystem. Each invitation sent out gets stored separately in the deployments subsystem, so it should be possible to come up with a feature to change invitations in between deployed participants. Similarly, there may be a need to modify invitations depending on subgroups, etc.
It should thus be possible to implement this as a feature fairly easily, though it warrants some thinking on how to keep track of that if there is ever a need to link up invitations (different versions as managed in the studies subsystem) to participants; or, perhaps that's not a real requirement.
There was a request to change the study invitation after a study has gone live.
Currently, it is locked in by design, since modifying it after going live requires further consideration: