You might be able to raise the mute on the offending side by loosening the screw that holds it down on the corresponding side. Sounds to me someone setup this Jaguar and did not take into consideration that the neck shim they used was either A.) Too high for the mute, or B.) the mute needs adjusted to push upward more.
The Jaguar mute is a finicky device, I installed one on my CIJ back in 2007 and used it for awhile but found it a bit annoying because you actually HAVE To shim the neck to make it usable as the bridge has to be raised to clear the screws that hold the mechanism on. I'm toying with building a second Jaguar in the future with a RECESSED vibramute to test out the idea of improving the design because I really do like what the vibramute offers, but I like how Jaguars play (really low, slinky, and fast) without a shim.