The rebuttal is a DMCA Counter-Notification. They're easy to write and just asset that you do in fact own the copyright, or are otherwise authorised the use the materials that the DMCA notice referred to. Once that's been done, the host has to restore the removed content within a certain time period and the issuers of the original notice have to take action directly against you (as in sue you) if they want to pursue the issue further.

Before we start yelling about "abuse of process" though, we might want to wait for more information about what's actually going on here. It would hardly be the first time one small company has used another company's assets without permission, so perhaps we should see what LayerVault has to say before getting so worked up.