Please show the images.
This might be anything from "layers intact" to "not simply traced but drawn manually". depending on the source files.
Autotracing will create shapes that don't overlap. but this artwork could be created easily by drawing a grid and then adding the graphs to that. So that when deleting the graphs you won't get any gaps in the grid.
To have this structures sensibly you could put the grid and the text on one layer and the graphs on another one. You could fine tune this even further.
Maybe you just send the file to your client and ask them?