Nice question. I guess, being able to understand the structure of a sentence can be helpful here. To that end, being able to cut out the fluff may make it easier to judge whether the foundation of the answer choices still "works". Will be focusing on structure going forward, though I'm sure some of you see the possessive apostrophe issue as well
In 1982, archaeologists recovered Henry VIII's ship Mary Rose, which, having sunk in 1545, with more than 17,000 artifacts on board, everything from arrows and longbows to a barber-surgeon's chest containing items commonly used by sixteenth-century medics.
(A) In 1982, archaeologists recovered Henry VIII's ship Mary Rose, which, having sunk in 1545, with more than 17,000 artifacts on board, ---- Nope. A recovered M, which... what?
(B) Henry VIII's ship Mary Rose sank in 1545 and, recovered by archaeologists in 1982, they found more than 17,000 artifacts on board, ---- > M sank in 1545 and THEY(?)... I guess you could try to make an argument that THEY refers to archaeologists but the structure still doesn't hold.
(C) When Henry VIII's ship Mary Rose, which sank in 1545, was recovered in 1982, archaeologists found more than 17,000 artifacts on board, --->.... When A was recovered, B did.... Not bad.
(D) Having sunk in 1545, Henry VIII's ship Mary Rose was recovered in 1982 by archaeologists, finding more than 17,000 artifacts on board, with ---- > On my V48 I got didn't get a single counted SC wrong. Even now, I still wonder if HAVING has this element of causation, though I'm not absolutely sure how the GMAT looks at it. The GMAT may only think of HAVING as referring to something that happened previously. In either event in terms of structure FINDING doesn't link well with the previous clause.
(E) Finding more than 17,000 artifacts on board, Henry VIII's ship Mary Rose, which sank in 1545, was recovered in 1982 by archaeologists and it had ---- The easy option to rule out. The ship didn't find anything. There is also a "is this really what the sentence would structurally want to say issue" with the usage of IT in that spot.
Ans. (C)
All the best.