The correct answer is D) bluing the teeth. After the reduction gear housing has been bolted down, the final check of the reduction gear tooth contact is typically done by applying a blue layout dye or "bluing" to the teeth. This allows the technician to visually inspect the contact pattern on the gear teeth, ensuring proper fit and alignment. Bluing the teeth is the standard method specified in Coast Guard regulations for this final inspection step. The other options, while potentially used in other gear inspection or maintenance procedures, are not the typical method for the final tooth contact check after the reduction gear housing is secured. Dial indicators, alignment gauges, and bridge gauges may be used earlier in the installation process, but bluing the teeth provides the most direct and reliable way to verify the proper tooth contact pattern.