Since this doesn't happen with other xtals, we'll assume your measurement deck is OK.
Spurs in crystals occurs more often than not, however, some crystal batches show poorly. I had 1 set of 4.952 MHz xtals where multiple spurs lie 50 KHz apart up from center when swept in a tracking gen and spectrum
My sweeps skirt looked jagged on the high side of Fs in my homebrew sweep system. I ordered another batch. They were fine and I threw the others in the rubbish.