How to Remove or Edit Unselectable Fixed Green Line in InDesign Document?

It looks like a guide. You can normally select those, either by clicking on them or dragging across them. On a Mac you can select all guides on the active spread with Command-Option G. On Windows probably with Control-Alt G.

The guides might be on the parent page, in which case they are not selectable on the current page without overriding them. Overriding and delting the guides will only remove them from the current page. Other pages based on that parent page, and hte parent page itself, will still have the guides.

To remove the guides from the Parent Page go to the Parent Page in the Pages panel and repeat the above process to select and delete guides. To override the guides on only one page you can Command-Shift (Mac) or Control-Shift (Windows) click on them to override and select them, then delete.

Check your preferences for any recolored guide settings (Unlikely, but you can check the Grids section too.)

Make sure your guide(s) are not locked: 

• View>Grids and guides>Lock Guides
• Layer panel for locked layers (guides are created on a per-layer basis and may be on a locked layer)
• Check all layers in panel for the following setting:
  

Check your parent pages for guides. If using based-on pages, you need to check the main parent. 

It also could be a guide. Check if the guides are locked: View menu > Extra > Guides and grid

Have you tried going through Object>Unlock All on Spread on either the document pages or any Parent Pages that might be applied to see if that allows you to select the lines? 

It is not enough to be seen on your image.

Did you look on the parent page or a parent page of the parent page?

Are alll layers unlocked?

If nothing is to see, export the file as IDML, open that and asve it as a new INDD. Maybe it disappears or it is at least possible to select now and to delete.