Try orienting the machine so that the headphone jack is at the bottom. Shake vigourously, perhaps with some gentle tapping near the jack, in an attempt to dislodge the debris.

You could also try a blast of compressed air. Or a fine probe, pick, awl, scribe, needle, wire, fishing hook, tweezers, etc. The chip of "mothball" packaging/dessicant stuff is probably soft and mushy, easily picked and carved out with whatever tools can reach it. If it doesn't come out clean (in one piece) then let gravity pull all the bits and crumbs and dust-like particles out of the jack for you, don't want that toxic crud jammed inside your machine.

You could try spot-cooling to harden it, or spot-heating to soften it ... but don't melt it!

Take care to not damage the headphone jack itself or the chassis plastics which surround it (which you could cover with masking tape to protect vs scratches/etc).