Got CNA, but the DTS rate is way higher than booking directly with hotel.

Good afternoon Team,

I got CNA so I can book for the per diem rate, however, all the hotel options in DTS is at least 50-100 dollars more expensive than per diem rate. I looked up the hotel website and seems like I can literally book with the per diem rate. Can I book through hotel directly using GTCC and get reimbursement? If I do book through hotel, how do I start the paperwork?