Frequent time window changing disruptions result in high secondary delivery rates in the last mile delivery. With the rapid growth of parcel volumes in online shopping, the time window changing disruptions could translate to substantial delivery cost-wastes. In recent years, customer pickup (CP), a new delivery mode that allows customers to pick up their parcels from shared delivery facilities, has provided a new way to deal with such disruptions. This study proposed a disruption recovery problem with time windows change in the last mile delivery in which customers can be served through home delivery (HD) or CP. A variant variable neighborhood descent (VVND) algorithm was presented to solve the problem. Computational experiments based on a set of instances were tested, and results were compared with other heuristics in the literature, which have affirmed the competitiveness of the model and algorithm.