I'd like to propose another way of doing it:

Do a PointOnAreaOverlayer of the points on the bounding polygons, have it make a list on the points and then use a ListIndexer with index set to 0 to promote the attributes from the first list element to attributes of the feature itself, then remove the list. That way each point will only belong to 1 polygon, even if it's exactly on the border.

Thank you for your answer. I think this idea can works, but our context is specific. First, the input point data can be in pgpointclouds format(https://pgpointcloud.github.io/pointcloud/) . This format is not directly compatible with FME. Second, the amount of point data is very big and the process have to be fast. I faced limit in treating big amount of data using FME (too long time running process). I rather use SQL and PDAL Library when for spatial operation dealing with big amound of points. These technics are faster in our context, but more complex and less flexible than FME. That's why I would like to withdraw the topology using FME (without creating hole between bounding box, of course), but I'm not sure it is possible. ?

I wouldn't recommend leaving gaps between the bounding boxes as this would introduce the possibility of points going missing.

Instead of the PointOnAreaOverlayer you could try the Clipper, in broad terms they work the same (they both have an option to speed things up by having the areas go in first) but there might be some performance enhancements under the hood that @mark2atsafe​ can shed some light on.

thank you for your answer. I won't change the geometry of the bounding box finaly. Consequently, my process are more complex, but this is better than loosing points ^^.