In a routed configuration, what does LTM do with the packet before sending it to the pool member?

Changing both source and destination IPs describes full NAT or SNAT combined with DNAT - in a basic routed configuration only the destination IP is changed by default.

Leaving the packet unchanged would mean the pool member receives a packet destined for the virtual server IP, which it would not accept since it does not own that address.

Changing only the source IP describes SNAT behavior, which is a separate optional feature - the destination IP must be changed to route the packet to the correct pool member.

In a routed (full proxy) configuration, clients send packets to the virtual server IP address. Before LTM forwards the packet to a pool member, it replaces the destination IP address with the pool member's real IP address. The source IP address is preserved (unless SNAT is also configured), so the pool member receives the packet appearing to come from the original client.