An assembly is provided for a gas turbine engine. This engine assembly includes a gas turbine engine case, a conduit and a bushing. The gas turbine engine case includes a case wall and a boss at a port through the case wall. The conduit extends longitudinally along a centerline through the port and into an interior of the gas turbine engine case. The bushing circumscribes the conduit and is arranged within the port. The bushing is engaged with and laterally between the conduit and the boss. The bushing is configured from or otherwise includes a cellular material. The cellular material may be or otherwise include a cellular metal material and/or a cellular composite material.