What does 'reghosted' mean in a seismic cube label?
As you rightly say, data will normally be deghosted during processing.

However, sometimes the deghosting is performed by the acquisition company rather than the processing contractor. The most obvious example would be PGS Geostreamer data, where 'raw' field tapes supplied by PGS to the customer are the upcoming wavefield, with the receiver ghost already removed. This is because the process of combining the velocity sensor and hydrophone data to remove the sea surface reflection is PGS's secret sauce - in many ways building a multi-sensor streamer is the easy part. They work with the true raw data internally, but never supply it to anyone else.

This is normally fine, but if the data is later processed (or reprocessed) by someone else, then complications can arise. If this other processing company wants to perform Full Waveform Inversion, which involves modelling a synthetic wavefield and comparing to the recorded wavefield, then the absence of the receiver ghost will cause an issue. Since the boundary condition at the sea surface has to be reflective to model the multiples correctly. Thus, they may add the receiver ghost back into the data by making an assumption of the sea surface reflectivity and adding it back, creating a 'reghosted' dataset to compare to the synthetics within the FWI.

That said, this would be an internal working dataset for the processing company, not something that would be supplied to the client. So I am surprised you would come across it without knowing what it was, if you see what I mean.