There is no such thing as a TCP/IP packet. Ethernet is only for the LAN, hence the MAC/Ethernet address (and the Ethernet header that contains it) doesn't get routed. Routers only route IP addresses, and see you can see that the IP packet header doesn't have a MAC address field. When a router receives an IP packet (which will contain other data from higher OSI layers relevant to other aspects of the interaction), it inspects the Destination Address header. It then inspects its routing table. If the address in that header is "known" (because it is on a local segment) then it will unwrap the message from the IP packet and wrap it in an Ethernet frame with the destination MAC address, then forward it onto the LAN via the relevant local port to be received by the target host. If not it will forward it to the appropriate IP address/router according to the data in its routing table. This "appropriate" address might just be the default route.

There is no such thing as a TCP/IP packet. Ethernet addressing is only for the LAN, hence the MAC address (and the Ethernet header that contains it) doesn't get routed. Routers only route IP addresses, and see you can see that the IP packet header doesn't have a MAC address field. When a router receives an IP packet (which will contain other data from higher OSI layers relevant to other aspects of the interaction), it inspects the Destination Address header. It then inspects its routing table. If the address in that header is "known" (because it is on a local segment) then it will forward it onto the LAN via the relevant local port. If not it will forward it to the appropriate IP address/router according to the data in its routing table.