The couple recently purchased the Brentwood property and the low-key stars promptly got to work on protecting their privacy by installing a nine-foot (2.74-metre) tall gate to shield their home from prying eyes.
However, one local has taken issue with the new blockade and has filed a complaint with the Los Angeles City Department of Building and Safety, claiming it violates the legal limit of six feet (1.83 metres).
Local officials have confirmed they are investigating the allegations. Paltrow and Martin will have 45 days to fix any violations or face fines of more than $900 (£580), reports Tmz.com.
The Iron Man actress recently admitted that she would love to temporarily relocate from the family's London pad to her native California, so her son Moses, seven, and daughter Apple, nine, can experience new adventures on the west coast.
She told Harper's Bazaar magazine, "Just to have my kids be in the sun every day - picking avocados, going for a swim... Even for two years or something, and come back (to the U.K.) when they go to senior school."