How does TCP manage to discard segment received from a source other than the one with which the connection has been established? It is known that TCP is a connection oriented transport layer protocol of the TCP/IP suite. But TCP (and UDP) operate over a connection less network layer protocol, the IP (internet protocol). What this means is that in TCP, if a sender sends data to the receiver, at the network layer, the receiver will accept the packet, without bothering about the source IP address of the packet. The receiver network layer then strips-off the IP-header from the received packet (and the IP address information of the source and the destination get stripped along with it), and passes off the remaining segment to the transport layer.

Now the doubt arises is, since the IP address information has been stripped away from the packet before forwarding it to the transport layer, how does the TCP sitting at the transport layer manage to decide from which IP address the information has come, when the only address details the transport header contains is the source and destination port numbers of the processes running on the respective hosts?
"Stripped away" is not strictly correct. A TCP packet is an IP header followed by the TCP-specific data. The IP-level information is needed, and used. In particular, the source IP address is needed (as you say) to decide which currently open TCP conversation should receive the packet that has just arrived.