Two delegations of Japanese officials visited Palisades Park, N.J., this month with a request that took local administrators by surprise: The Japanese wanted a small monument removed from a public park.

The monument, a brass plaque on a block of stone, was dedicated in 2010 to the memory of so-called comfort women, tens of thousands of women and girls, many Korean, who were forced into sexual slavery by Japanese soldiers during World War II.

But the Japanese lobbying to remove the monument seems to have backfired — and deepened animosity between Japan and South Korea over the issue of comfort women, a longstanding irritant in their relations....