How do you remove only the conditional formatting from a cell and leave all other formatting intact?

This is not possible-you can remove only all formatting from a cell.
Select the cell. On the Home tab, click Conditional Formatting > Clear Rules > Clear Rules from Selected Cells.
Right-click the cell and select Delete Conditional Formatting.
Right-click the cell and select Remove Conditional Formatting.

The correct answer is:

Select the cell. On the Home tab, click Conditional Formatting > Clear Rules > Clear Rules from Selected Cells.