Here is how I understand "pickup", in this context.
Suppose that two nodes (nets) in IC design are supposed to be completely decoupled - i.e. thay are supposed not to "see", not to "feel" each other.
I.e. when voltage or current on/in one of the net changes - this does not affect the other net.
But in reality, in physical implementation of IC, parasitic elements - parasitic resistors in the metallization, parasitic capacitances between nets, parasitics resistive and capacitive (mostly p-n junctions) elements in the substrate, parasitic inductances and inductive loops - lead to interaction between the nets.
So, when a noisy net changes its voltage or current, it affects other nets, coupled (by parasticis) to it - and their electrical conditions (voltage, current, etc.) change, in response.
This unintended coupling and electrical change, caused by other nets, is called "pickup".