Everyone must have a link back to you (or the person with whom you started your tree). Either a blood relative or by partnership (marriage, relationship, engaged,...).
When you made them partners, did you select "Partner with someone already on tree" or "Add new partner" / "Add new ex-partner"?
When you created the partnership, if you selected "...already on tree", these are the steps to take:
1. Select one of the people (doesn't matter which one).
2. Select the Partners tab (in the sidebar on the left); see the partnership you want to remove.
3. Click "Change or delete" at the bottom of the list of buttons.
4. Click "Change partner"
5. Click "Set no current partner"; partner will now be listed as Ex-partner
6. Again, in the Partners tab, click "Change or delete" at the bottom.
7. Again, click "Change partners"
8. Click "Remove ex-partner <partner's name>"
The partnership should be gone.
When you created the partnership, if you selected "Add new partner / ex-partner", you'll need to establish a link between that person and someone in the tree before you can remove the partnership. Otherwise, you'll have to delete the partner.