A method and system for a base station to manage air interface communications with a wireless client device (WCD) served by the base station, taking into account whether the WCD is a relay-WCD that provides wireless backhaul connectivity for a relay base station. The base station will determine whether the served WCD is a relay-WCD, and based on a determination that the served WCD is a relay-WCD, the base station will responsively invoke a process to help expedite air interface communications with the served WCD, in an effort to reduce the total delay resulting from the wireless relay arrangement. In particular, based on the served WCD being a relay-WCD, and perhaps based on the relay-WCD facilitating a threshold extent of delay-sensitive communication, the base station will invoke transmission time interval (TTI) bundling, to help expedite the air interface communications between the base station and the relay-WCD.