In our view, the best approach is to finish out the hole, and the coaching voice in us says to take the learnings from each shot rather than always thinking about your score for that hole.
The Strokes Gained model we use to analyse a golfer's game talks a lot about ensuring every shot counts. It's even the title of Strokes Gained pioneer Mark Broadie's book - Every Shot Counts.
When looking to improve, how do we know if your strengths and weaknesses in putting or in the short game if you're picking up regularly and not getting into those zones.
If this truly isn't an option, the next best option is to repeat the entire previous hole so you have a complete hole entered of relevant data.