Given that the people you’ve seen carrying rosaries at Communion are generally older, it probably is a remnant of a time when laity would pray the rosary during Mass. This was never mandated by the Church, it was instead a pious custom, but it gained popularity among the faithful because the older liturgical rubrics of the Mass allowed for far less lay participation in the Mass than they do today.
Because the laity generally had little to do but follow along in a missal while the priest offered Mass, some began to pray the rosary as a way of participating at Mass. This custom was never a good idea because the rosary is a private devotion and the laity’s attention should have been focused on the public prayer of the Mass. One positive result of the reform of the liturgical rubrics is that it is now easier for the laity to more fully participate in the celebration of the Mass in a manner proper to their status as laypeople.
Those who grew up with the Tridentine Latin Mass have sometimes brought to the reformed standard rite of the Mass pious customs that they became attached to in their youth. That is why you will sometimes see elderly women wearing veils or hats (which is a good pious custom because it derives from ancient Church discipline) and why you will sometimes see elderly people praying the rosary or carrying it during Communion (which is something that is not a good idea for the reasons outlined above).
