How should I go about refitting the seal under this interior door?
As you can surmise it is difficult to see under the door to evaluate what is going on with this plastic strip. Even if you had a good understanding of how the seal was originally secured in place it would be extremely difficult to get tools and possible supplies up under the door to work the seal back into place. 

So it really comes down to taking the door off its hinges and setting it down on it's side so that you can inspect and take action to fix the problem. Once things are more fully understood you are in a lot better position to take the next steps actions. 

Depending upon the situation be prepared that it may be necessary to re-hang and remove the door at least one additional time if it is necessary to procure supplies or delay the actual repair work.