I've used a system of sequence numbers/tombstones/etc. like in common directory services to sync the data when I developed such a sync-functionality.
It's easy to implement and the amount of traffic commonly is very low - as it only transmits the sequence numbers for unmodified entries.
At least if you local database isn't empty or very old.
[e]
You could also compress/pack the string data. There are lots of pre-made algorithms out there.
Like
https://github.com/antirez/smaz/tree/master
'This is a small string' compressed by 50%
'foobar' compressed by 34%
'the end' compressed by 58%
'not-a-g00d-Exampl333' enlarged by 15%
'Smaz is a simple compression library' compressed by 39%
'Nothing is more difficult, and therefore more precious, than to be able to decide' compressed by 49%
'this is an example of what works very well with smaz' compressed by 49%
'1000 numbers 2000 will 10 20 30 compress very little' compressed by 10%
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