For most cases the JBrowse data is pre-processed in such a way that it is not really easy to re-download it as a GFF.

JBrowse does allow generating a GFF from particular regions of the file via the "Save track data" function but that is not the full track data or the original track data even

If you want the original track data it is probably important to have the jbrowse admin provide this externally

Newer versions of jbrowse are working towards loading the original track data directly rather than pre-processing e.g. using indexed formats like tabix vcf/gff/bed, bam, bigwig, bigbed, etc. so then the original track data displayed in the track is already the original source data, so that will make this easier in the future.