The Spider Queen is a spider found in the 2009 Hallowe'en event which has sent a giant spider into the Grim Reaper's bath tubs. She was offended that the Grim Reaper took the cob webs out of his house and asks you to put them back. She gives you a spider called Eek to help you do this who you can keep at the end of the quest. She also gives you your final reward of a Web Cloak when you complete it.
Since time immemorial, Guthix has decreed that the Grim Reaper's role involve a particular aesthetic. The scythe! The hood! The bones! The Grim Reaper must have these things! The decor of his house is similarly prescribed. it must be dark. It must be ominous. It must be spooky. And it must have spider-webs! But the Grim Reaper has cleaned his house and removed all the spider-webs. At Hallowe'en, the most spooky of seasons! I take this as an insult! The bath spider will remain until the Grim Reaper's house is full of its proper cobwebs.