If you are talking about a SMPS (switch mode power supply) choke, if so it can be prefferable to remove copper from under the switching loops to avoid capacitive coupling of the switching noise to the planes for EMC purposes, and from under the magnetics to avoid magnetic coupling. Engineers have differing opinions on this and how much copper should be removed, so I should check with the circuit designer. All our SMD inductors for SMPS have no copper under them on any layer.
Actually i am placed common mode chock for lvds and HDMI nets those nets connected between qseven module and displayport and those nets are high speed differential nets.
Interesting, I havn't played with HDMI signals, I would check some HDMI guidelines.
Without further research I wouldn't like to give an opinion. If you look at Ethernet magnetics, they recomend removing copper from under the devices, but cant say for HDMI.