Word import into InDesign can be flakey, but there are a lot of things that can be tried to improve things.
First, be sure that ALL tracked changes are accepted or rejected. Next, do a Save AS in Word to force a file re-write.
If it does import correctly after that, try saving as .doc instead of .docx, or vice versa, or save as .rtf and import that. It sounds to me like the problem is with their people, not with you or what you've done.