Low Extra Delay Background Transport (LEDBAT) congestion control algorithm is designed to address the unfairness problem of TCP aggravated by applications that use multiple TCP connections for data transfer. LEDBAT operates under the assumption that the queue delay at the access router of the bottleneck link will be the primary varying contributor to end-to-end one-way delay. However this assumption will not hold if a route change occurs, which causes significant variations in the path delay. This paper analyses the impact of route changes on LEDBAT throughput and fairness. In addition to a formal description of the behaviour of LEDBAT congestion window when route changes, we present results from simulations showing the negative impact of route changes on throughput for a LEDBAT source and fairness with other sources. Importantly, our analysis shows that more work is needed to improve LEDBAT performance in the case of route changes before the novel algorithm can be considered as a suitable congestion control algorithm in the Internet.