grep: group capturing

This might work for you:

echo '{"_id":"scheme_version","_rev":"4-cad1842a7646b4497066e09c3788e724","scheme_version":1234}' |
sed -n 's/.*"scheme_version":\([^}]*\)}/\1/p'
1234

Sorry it's not grep, so disregard this solution if you like.

Or stick with grep and add:

grep -Eo "\"scheme_version\":(\w*)"| cut -d: -f2

You'll need to use a look behind assertion so that it isn't included in the match:

grep -Po '(?<=scheme_version":)[0-9]+'