score:7
Short Answer
The reference to "that famous east window on which Henrietta Maria had once cut her name with a diamond" seems most likely to be a conflation of two or more of various events and artefacts connected to Henrietta Maria and / or her husband, Charles I. These events / artefacts involve Henrietta Maria breaking a window, Charles I purportedly inscribing messages to her on glass with a diamond, a window with an anti-Henrietta Maria inscription made with a diamond, and a marble tablet with her name inscribed on it above a window.
Details
Although there does not seem to be any evidence that Henrietta Maria performed an act of 'petty vandalism' by using a diamond to carve her name, the following are certainly of interest:
Henrietta Maria is recorded as breaking a window with her fists (Harley Mss 383, f. 33., in the British Library) when she learned (in 1626) that most of her French servants were being dismissed by Charles I (whom she had married in 1625). The entry reads:
It is said the Queen, when she understood the designs grew very impatient and broke the glass windows with her fists...
Cited in Carolyn Harris, 'Queenship and Revolution in Early Modern Europe: Henrietta Maria and Marie Antoinette' (2016)
Charles I is purported to have used a diamond to inscribe romantic messages (and his initials) to Henrietta Maria on diamond-shaped glass panes. Although there is no evidence that Charles is the author of these messages, C. S. Lewis may well have been aware of this attribution. This from the Victoria and Albert Collection:
This panel comprises nine quarries (small diamond-shaped panels) of green tinted glass, each diamond engraved with an inscription. They are purported to have been written by Charles I (1600-1649) to his wife Henrietta Maria (1609-1669) on the window of his prison at Carisbrooke Castle on the Isle of Wight, where he was detained in 1646. There is, however, no evidence to support this supposed provenance. The glass is hand blown and extremely thin, qualities compatible with a 17th-century date.
There was a story of an 'anti-Henrietta' inscription, made with a diamond, on a windowpane in Whitehall.
Perhaps there had come to the ears of the little heir [the future Charles II] the story of the inscription scratched with a diamond upon a window-pane at Whitehall. "God save the King" so it ran "confound the Queen and her children,..."
Source: Ida A. Taylor, 'The life of Queen Henrietta Maria' (1905)
A final thought which may or may not be relevant: the passage in C. S. Lewis's That Hideous Strength which mentions Henrietta Maria and the window inscription appears in a chapter titled 'The Liquidation of Anachronisms'. The chronological aspect that Lewis might be getting at seems obscure, but he could possibly have invented an anachronism relating to a diamond signet Charles I gave his wife about two years after their marriage by substituting the window breaking incident with using the diamond signet to inscribe her name. However, this is admittedly highly speculative and Lewis may not have intended an anachronism when writing "that famous east window on which Henrietta Maria had once cut her name with a diamond."