Many people do not understand the legal difference between ownership of a painting and ownership of its copyright. The purchaser of a painting does NOT own the copyright unless the artist also transfers said copyright to the buyer. Even though the original artwork is in your possession, the artist may continue to make and sell prints or giclees, and give permission for others to reproduce the artwork in books, magazines or web sites. You, the owner, may not do any of these things unless you also obtain permission from the artist.
If the photo (reproduction) of the artwork is posted on a website without permission, only the artist can request that it be removed or, if necessary, pursue legal remedies. If this matter concerns you, bring it to the attention of the artist, his gallery or his legal representative. If the web site exists for educational purposes, the "fair use doctrine" of copyright law may cloud the issue.
Most artists would likely ignore the web site's posting, considering it free advertising, or perhaps request the site to add a link to the artist's gallery or personal website.