Hi Will,
Data updates to your web service are going to take some time to execute, so in terms of providing the very best responsiveness to the user your best approach would be to fire these off on a background thread.
If updates not taking place (until your app resumes) due to a back press is a concern for your app then you can increase the frequency of sending these updates off.
Storing data locally would be a good idea following each change to make sure nothing is lost since you don't know if your app will get interrupted such as by a phone call.
You are able to intercept the back button which would allow you to handle notifying the user of pending updates being processed or requesting confirmation to defer transmission (say in the case of poor performing network location). Perhaps a visual queue in your UI would be helpful to indicate pending requests in your storage queue.
You may want to give some thought to the overall frequency of data updates in a typical usage scenario for your application and how intensely this would utilise the network connection. Depending on this you may want to balance frequency of updates with potential power consumption.
This may guide you on whether to fire updates off of field level changes, a timer when the queue isn't empty, and/or manipulating a different row of data among other possibilities.
General efficiency guidance with mobile network communications is to have larger and less frequent transmissions rather than a "chatty" or frequent transmissions pattern, however this is up to you to decide what is most applicable for your application.