I just finished ripping the back of my 2002 apart, the way I took them out was.
1. fold down rear seats.
2. remove rose buds (grey plastic grommets) from top deck and if the 03 has the interior
brake light, take that out too (lightly pull on it, its only clipped in).
3. I don't know if this is nessasary but I had the centre molding behind the seats
already off
4. slide your hand under the plastic-carpet and gently lift bowing it until the corners
are free, then pull forward removing the piece from your car
5. I think the bolts are 12mm but I could be wrong. There are 3 bolts per speaker.
I might have left out some minor details, like taking headrests off or the child safty anchor covers, but from what I remember this is the basis for operation. As far as taking off the grilles, I don't think you can. I can't see your '03 being too much different. Have fun