Functional imaging studies of episodic memory retrieval consistently report task-evoked and memory-related activity in the medial temporal lobe, default network and parietal lobe subregions. Associated components of memory retrieval, such as attention-shifts, search, retrieval success, and post-retrieval processing also influence regional activity, but these influences remain ill-defined. To better understand how top-down control affects the neural bases of memory retrieval, we examined how regional activity responses were modulated by task goals during recall success or failure. Specifically, activity was examined during memory suppression, recall, and elaborative recall of paired-associates. Parietal lobe was subdivided into dorsal (BA 7), posterior ventral (BA 39), and anterior ventral (BA 40) regions, which were investigated separately to examine hypothesized distinctions in sub-regional functional responses related to differential attention-to-memory and memory strength. Top-down suppression of recall abolished memory strength effects in BA 39, which showed a task-negative response, and BA 40, which showed a task-positive response. The task-negative response in default network showed greater negatively-deflected signal for forgotten pairs when task goals required recall. Hippocampal activity was task-positive and was influenced by memory strength only when task goals required recall. As in previous studies, we show a memory strength effect in parietal lobe and hippocampus, but we show that this effect is top-down controlled and sensitive to whether the subject is trying to suppress or retrieve a memory. These regions are all implicated in memory recall, but their individual activity patterns show distinct memory-strength-related responses when task goals are varied. In parietal lobe, default network, and hippocampus, top-down control can override the commonly identified effects of memory strength.