Two options come to my mind immediately;
[list=1]1_You have a normal subD conversion that filters the topology display in order to catch the curvature.

2_You have some orphaned vertices (Vertices that remain after you delete an edge intersecting another one) And it is taking it in account.[/list=1]

If you haven't come cross it earlier a SubD can seem to do funny things to the wireframe via conversions. Sort of looking more like an Aztec work of art rather than a wireframe. If it is something like this don't worry about it. Just clean the model a bit better the next time before you convert it if you don't like the looks of things. Like watch to make sure the faces are planer and not n-sided (more than 4 sides) But if it isn't bothering you and it is a seriously complex structure all together.. leave it. Won't really ruin anything.

As for if you have extra vertices that have no serious use; Just select the whole object and press delete. MaYA only removes orphaned ones as they have no dependency layed on them.
Important note!! Orphaned means a vertice on an edge with no other connections. This means a total of maximum 2 connections. A vertice on the corner of a plane (Not a cube) ALSO has 2 connections only. So if you have an open mesh constructed of planes; then you may want to unselect the ones in the corners.

Shall it be that your problem is neither of the above; you have to post a sample picture for us to be able to help you on it. Or at least myself. I can't think of another reason that fits the discription.