This building is thought to have got its name from a William Gryge who lived in Godalming in the reign of Richard II. It may be that the building was associated with him and got its name that way. Certainly, it had acquired the name of Griggs by 1598.
The first floor braces on the facade are bent like an elongated 'S' (=ogee braces). This style was in fashion in this area between about 1540 and 1590. So the building probably dates from that period.
Going back in time
For enlargements, click images
Image: Godalming Corporation 1937 Album p34e
The White Hart building and Griggs (97-103 and 105 High Street) in the 1930s
image: Godalming Museum, ref 3093
High Street in the 1901.
The large building on the right is the White Hart building (early 17th century) and on the extreme right is Griggs (late 16th century - note: the tops of the ogee beams that are now exposed were painted over at this time and the rest of them was hidden behind the top of the shop front)
image: from Old Cottage and Domestic architecture in South-West Surrey p24