The GS cup: David Mitchell (Silversmiths in Elizabethan and Stuart London, Woodbridge, 2017, pp. 312-3) discusses this mark 'GS' crook between, two pellets above, in plain shield, as attributed by Charles Oman (Caroline Silver 1625-1688, London, 1970, p. 40) to Gilbert Sheppard. Mitchell illustrates a near pair to the present cup (fig. 161) in the collection of the Worshipful Company of Goldsmiths.
The TC cup: Mitchell (o.p cit.) notes that the monogram mark is likely to be read as TC rather than CT and that there are three such marks between 1633 and 1686 but the shape of the shield is usually not recorded. The mark illustrated, (from Jackson's Silver & Gold Marks, Woodbridge, 1989, p. 119) has a flat top to the shield as opposed to the trefoil style top of the present cup.