Basic Answer for Returning
I would personally use option 2, which is: `A JSON object with one String attribute.'
Also, in terms of design: I prefer to return an object, that has a key/value. The key is also a name that provides context as to what has been returned.
Returning just a string, basically a "" or {""} lacks that context ( the name of the returned variable.
Debate: Are primitive Strings Json Objects?
There seems to be also some confusion as to if a String by itself is a valid JSON document.
This confusion and debate, are quite evident in the following posts where various technical specs are mentioned: Is a primitive type considered JSON?
The only thing for sure is that a JSON object with a key-value pair is definitely valid!
As to a string by itself.. I'm not sure ( requires more reading).
Update: Answer In terms of creating/updating an entity (Post/Put)
In the specific case above, relating to such a large string that "runs into a few kilobytes"... my feeling is that this would be included within the request body.
In the specific context of sending data, I would actually be comfortable with using either 1 or 2. Additionally, 1 seems more optimized ( if your frameworks support it), since the context about what the data is, is related to the rest API method.
However, if in the future you need to add one more parameter, you will have to use a JSON entity with more than one key.