Step 1: Identify the disputed islands.
The Senkaku Islands (called Diaoyu Islands in China) are a group of uninhabited islands in the East China Sea. Both Japan and China (and Taiwan) claim sovereignty over them.
Step 2: Eliminate incorrect options.
(A) Osaka Islands — Osaka is a metropolitan prefecture in Japan, not disputed islands.
(B) Muntheetu Islands — Not relevant in this context.
(C) South China Islands — refers broadly to the South China Sea disputes, but those are between China, Vietnam, Philippines, etc., not Japan.
(E) None of the above — incorrect since Senkaku is correct.
Step 3: Confirm.
The well-known territorial dispute is indeed over the Senkaku/Diaoyu Islands.
\[
\boxed{\text{Senkaku Islands}}
\]