First make sure that grid snapping is turned on - Grid -> Activate Then after picking up the object(s) to be moved (an Auto Probe on any end point will probably do it), use the Grid Probe to drop it. That's the third one down in the vertical menu of probe types.
You may need to zoom in a bit for this to work satisfactorily because there are some preference settings called "Probe radii" that affect how close to a selection you need to be to make it work. These settings also affect how the various probe types are ranked for an Auto Probe.
TBH this is how it was intended to work 30 years ago, it might have been changed since then