For a second there I thought Reimu and Marisa were both dead judging by the contents of Orin's wheelbarrow... but then Satori states that Parsee can go to the surface and meet the "real" Marisa. Unless Chihiro goes by the pichuuuun~ then respawn type of canon. So they did die, but they re-spawned back in their house/shrine.
Or if the "killed" Marisa is some fake created by Parsee's powers and Marisa's jealously of Reimu, that would still imply that Reimu is dead. Just what is going on in this doujin?
Base +6, onlyregistere +13, qwopqwop +9, Anonyslime +8
So, as far as I can tell, this is a different take on Parsee's power to control jealousy. Specifically, rather than making people feel envy, she can take that emotion and manifest it into a physical or semi-physical form, like she did in with Marisa. That would explain why Orin wasn't able to get an actual corpse. Since she was only controlling Marisa's jealousy, that manifestation didn't have any of Marisa's memories or abilities. And it seems like Parsee was enacting that sequence out of her own jealousy for surface youkai and humans, specifically Marisa.
Regarding the "retrieval," I think Satori and Rin were collecting the remains of the envy-manifestations. Satori reveals that Marisa is still alive, and she has her overcoat, broom, and satchel. Again, that's why Orin didn't get an actual corpse. Presumably, Parsee has been manipulating those jealous memories with Marisa several times, since the "ghost" only dropped her overcoat but Rin already had her broom and satchel. It also explains what Parsee meant when she said she killed "Marisa" several times already.
All that would suggest Parsee's magic really can create physical or semi-physical embodiments of people's jealousy that in turn can leave physical remains. Parsee probably also did the same with Reimu, creating a specter of her envy, though they obviously didn't go into what Reimu was jealous over. That would explain why Orin had Reimu's yin-yang orbs.
As for why she did it, that's the biggest mystery, since even Satori couldn't find out why when she read Parsee's thoughts.
Base +3, the missing link +5, CyberZero +7, qwopqwop +9, LunaOlm +4, aListers -4, Watsaz +9, Lucas Conceicao +5, Fofotron +6, jovdree +6
So this goes along the lines of, they can be defeated as many times as it takes, since they are incident solvers they are allowed to retry as many times as it takes. Instead of simply retrying, they pop up back alive somewhere else. When things get weird, always blame Yukari.