Pulsar timing arrays (PTAs) are being used to search for very low frequency gravitational waves. A gravitational wave signal appears in pulsar timing residuals through two components: one independent of and one dependent on the pulsar's distance, called the ‘Earth term’ (ET) and the ‘pulsar term’ (PT), respectively. The signal of a burst (or transient) gravitational wave source in pulsars’ residuals will in general have the Earth and pulsar terms separated by times of the order of the time of flight from the pulsar to the Earth. Therefore, both terms are not observable over a realistic observation span, but the ETs observed in many pulsars should be correlated. We show that pairs (or more) of pulsars can be aligned in such a way that the PTs caused by a source at certain sky locations can arrive at Earth within a time window short enough to be captured during a realistic observation span. We find that for the pulsars within the International Pulsar Timing Array (IPTA) ∼67 per cent of the sky produces such alignments for pulsar terms separated by less than 10 years. We compare estimates of the source event rate that would be required to observe one signal in the IPTA if searching for the correlated ETs, or in searching via the PTs, and find that event rates would need to be about two orders of magnitude higher to observe an event with the PTs than the ETs. We also find that an array of hundreds of thousands of pulsars would be required to achieve a similar number of observable events in PT or ET searches. This disfavours PTs being used for all-sky searches, but they could potentially be used target-specific sources and be complementary to ET-only searches.