Can you post a screen shot? Could be one of several different things.
You have to work with Paragraph styles in both, in Word and InDesign. But you have to set up the paragraph styles in both programs differently.
I think this happens to errors in your formatting by not using styles.
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I may have stumbled onto an answer for you.
I was experiencing the same problem. What I finally discovered is that the lines were appearing when I tried to convert the Word Text styles into my InDesign paragraph styles that I had already set up in my document. This was occurring whether I had hit the "Remove Styles", Preserve Styles" or "Custom Styles" in the Import Options Box.
So what I did to resolve the matter:
1) converted word file to .rtf (not really sure that is necessary though)
2) deleted all my pre-existing paragraph styles in my InDesign document.
3) Imported rtf file
4) Developed new paragraph styles as I needed them in formatting the imported copy.
It was a a little cumbersome and annoying but this approach seems to be working.
Still not sure of the underlying cause and would like to know for future.
But in the meantime, I hope this helps (although being almost a month late with the answer probably is a "too late, too little situation"?
Just change the the paragraph style in Indesign. The lines are coming from the imported Word style.
Here's how I resolved it. When you click "place" you'll see a checkbox that says, "Show Import Options." Check that. Go to the bottom where you see the "Import Styles Automatically" drop downs and choose "Redefine InDesign Style." That seems to have permanently fixed the problem.