that VW beetle is out of place, especailly with a Grossdeutschland divisional insignia, a heer formation used only on the russian front.
True But then again the host company for this event IS Grossdeutschland, plus many units and elements of units were pulled west for Nordwind. Besides by that time of year wasn't the remains of the unit in East Prussia? There was a lot of back and forth traffic and Parts of units were being constantly "borrowed" to form Kampfgroups where ever needed so is it likely or possible a small detachment was involved - yes.
Actually no, that particular formation never made it to the west.
German practise with weapons was to leave equipment behind when reforming elsewhere, and the Heer did not send regiments back and forth, usually once in a division a regiment stayed unless the formation was disolved. Division signs where repainted on such equipment.
I believe you are confusing the Fuhrer-Begleit-Brigade with GD since they were technically part of GD Corps, a formation that existed mostly on paper.
Fuhrer-Begleit-Brigade used a stalhelm as a divisional insignia, but not a white one (which was GD) but usually a blue one.
In any case, neither formation was part of the Nordwind operation (I assume this is the attack in Alsace) which were elements of the 25th Panzergrenadier, 47th Volksgrenadier and 7th Fallschirmjäger divisions.