“You now wonder how to address the pillow situation. It seems the woman has you at a clear disadvantage.”
The velvet pillow is a possession of Rose Lalonde's that has a recurring role in Homestuck, a plush purple pillow embellished with sewn-on buttons and trimmed with gold thread. It was first introduced
in Act 2 as a weapon of her mother's passive-aggressive ire (or, perhaps more realistically, a misplaced attempt at mother-daughter bonding) against Rose, whereupon she captchalogued it with the intent of later embroidering a poem in praise of motherhood in retort.
Rose vents her frustration on the pillow in Seer: Descend.
While this promise was never fulfilled, the pillow has made further appearances throughout the duration of Homestuck, first when Rose used it as an alchemy ingredient to create her velvet squiddleknit dress , and subsequently to express her frustration through the ancient and noble art of mashing one's face into soft pillows, first in Seer: Descend, then and then multiple times during Act 6.
Later, Jasprosesprite^2 removes one of the pillow's buttons to serve as a placebo remedy for Tavrosprite's cat allergies as seen here. Whether the pillow used for this was from the pre- or post-retcon timeline is unknown. Indeed, it is patently unclear what happens to a person's sylladex items after they have died or been prototyped.
As seen in this page, Jade possess a similar, green colored pillow, for use in conjunction with her crystal ball. Its relevance is probably minimal, although it could hint at the original purpose of Rose's pillow.