Yes they do, ask for it at counter, small bottles. Update: I was told in April 2021 the restaurants no longer sell jars of the mustard. Most restaurants do not know that and just tell you it is out of stock.
Most White Castles do have the Dusseldorf-style Mustard for sale in jars.
I'm almost positive they do
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Honestly I don't know if they do or not they used to
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