Many of the so-called Roman troops present in Britain upto the mid 5th century were not Roman at all. The vast majority of them were Germanicor Gallic auxillaries. Traces of their worship may be found in ancient Roman sites including Hadrian's Wall in Northumberland.
"Teutonic soldiers serving under the Romans in other provinces of the Empire may also have worshipped their ancestral gods beyond the borders of their own native land. That such was actually the case is shown by two inscriptions of the third century, found in 1883 at Housesteads in the north of England, near the wall of Hadrian. The altar on which they are found was erected by Frisian soldiers from Twenthe,- which is rather strange inasmuch as Twenthe belonged to the territory of the Salic Franks,- and is dedicated 'Deo Marti Thingso et duabus Alaesiagis Bede et Fimmilene.' The relief above the altar shows an armed warrior with helmet, spear, and shield, at whose right a swan or goose is seen. Both of the receding sides (the relief is semicircular in form) shows the same figure of a hovering female, with a sword (or staff) in the one hand and a wreath in the other.
"What we do know is that the Frisian cuneus, encamped in Britain under Alexander Severus, worshipped Mars, ie Tiu, doubtless as god of war, as the armed figure in itself indicates. A fragment of nature mythology, according to some scholars, lies concealed in the swan, to be interpreted as the symbol of either light or cloud, and to be brought into connection with the Swan-knights of legendary lore.
"It appears likely that the Frisian cavalrymen, who call themselves citizens, saw in Tiu the god not only of the squadron but also of their popular assembly, the thing, and that the two side figures are to be regarded in the same light, their names having been explained from certain forms of Frisian legal procedure. However that may be, the fact that theses Frisian soldiers worshipped Tiu does not seem to show conclusively that this god of the sky was originally the chief god of all Teutons." (The Religion of the Teutons, Saussaye)
Anne Ross in her Pagan Celtic Britain considers the 'swan' to be a goose:
"The goose is a bird associated with war in Celtic mythology, and the Germanic god Thincsus, equated with Mars at Housesteads on Hadrian's Wall, likewise has the goose for attrribute.
She also comments:
"Mars Thincsus would seem to be the only non-Roman god to figure as an orthodox Roman warrior.
"It has been noted already that the Germanic god, Mars Thincsus who is invoked along Hadrian's Wall, is frequently accompanied by a goose.
"The goose is the frequent companion of Mars Thincsus in the northern frontier region.
"The goose appears below a representation of Mars on a slab from Risingham, Northumberland, erected by the Fourth Mounted Cohort of Gauls. The bird also accompanies what is taken to be a representation of Mars Thincsus (a Germanic god) at Cilurnum (Chesters) on Hadrian's Wall."
It would seem that amongst the Teutons and Gauls the goose frequently accompanies their war God, who is often equated with the Roman Mars.
"In Gaul, the native Mars is frequently associated with the goose and the horse, and Epona, the horse-goddess rides a goose on the fourth century tile from Roussas." (Ross)
Ross also mentions that the "bird appears with Mars on a stone from Iggelheim" and states that "all the evidence suggests that the goose was especially associated with the god of war and probably healing in Celtic belief, and that this idea either entered the Germanic traditions through Celtic influence, or was likewise indigenous to them."
Rudolf Simek in his Dictionary of Northern Mythology compares Mars Thingsus with Mars Halamardus, who is referred to on a votive inscription from Horn near Roermond in the Netherlands, dating most likely from the first century CE. He also points out that Thingsus is derived from the Proto-Germanic *Thingsaz and accepts that the associated names of Beda and Fimmilena are associated with Old Frisian legal terms so one may conjecture that these are obscure Frisian Goddesses. This adds weight to the argument that Mars Thingsus is Tiw, the God who presides over the sacred Teutonic Thing. Beda may be linked to the Old Frisian Bodthing ('convened Thing'). In other words She is 'the mistress of the *Bedthing*' (Simek). Fimmilena is likewise the 'mistress of the Fimelthing' ('moveable Thing'). Gudmund Schuette however conjectures that She is the 'goddess of Fivelland' but Simek rejects this interpretation. The Goddess Beda also had a cult centre in Bitberg on the German-Belgian border. The Roman name for this city was Beda Victus ('village of Beda'). It is interesting that these two Goddesses who are collectively called the Alaisiagae have both a Celtic and a Germanic etymology which is not surprising since Beda Victus continually was overrun by both Celtic and Germanic tribes.
Gudmund Schuette in his Our Forefathers the Gothonic Nations Volume 1 however considers that the "etymology of the word 'Thingsus' is uncertain; it may come from Langbd. thinx 'law thing', or from Got. theiwo 'thunder' ". The Low German Dingsdag (modern German Dienstag-Tuesday) does (as Schuette concedes) derive "from Mars Thingsus as the god is called by the Tvihanti from the province of Twenthe."