We do not have access to the code that is writing the data. You need to work with your application developers. They could write to:

• A bookmark
• A document variable
• A document property
• A content control

Instead, they are apparently writing to a legacy formfield with a given bookmark name. Unless their code is changed, that is where it will write.

A legacy formfield is not an ordinary Word field. (MS has a long practice of using confusing names.)

You could insert a legacy formfield with the bookmark and format it as hidden using the font formatting dialog. How that would work I have no idea.