What does the 'modify' option mean when I open the menu for the current stay? Does the owner get to confirm the modification?

Cost adjustments are best made before both you and the client accept the booking. If your stay ends early or needs to be changed you can use the modify function, see this article https://support.rover.com/hc/en-us/ar... and this one https://support.rover.com/hc/en-us/ar...

if you need to add a day to the booking use the extend stay button. And finally, as a new sitter, I highly recommend you spend lots of time in the help section and read, read, read so you become knowledgeable on how the platform works. Best of luck

I don't think it's really a good idea to charge more or less depending on the dogs behavior/how hard or easy they are. You can charge more for puppies but adult dogs should all be the same, the only exception I can see is a dog that needs significant medical attention.

You can however modify the booking if they came back early or needed to be gone longer.