A technique dynamically triggers an exchange of reachability information between a tail-end (remote) domain target node (e.g., a tail-end node) of a traffic engineering (TE) label switched path (LSP) and a local domain head-end node of the TE-LSP in a computer network. The inter-domain information retrieval technique is illustratively based on triggering a Border Gateway Protocol (BGP) session whereby at least a portion of the reachability, i.e., routing, information of the tail-end node is transmitted to the head-end node of the TE-LSP in accordance with BGP. Specifically, once a TE-LSP is established between the head-end node and the tail-end node, the head-end node triggers the tail-end node, e.g., through extensions to a request/response signaling exchange, to establish the BGP session. Establishment of the BGP session enables transmission of the routing information from the tail-end node to the head-end node. The head-end node uses the routing information to calculate routes, i.e., address prefixes and associated attributes, reachable from the tail-end node for insertion into its routing table.