You'll not only need to select the path in the paths dialog, and click on it to make it visible, and edit with the Paths Tool, as per @xenoid's instructions, but you will also need to make a new mask from the path after you've edited it. Deselect the selection by pressing Shift+CTRL+A (Select None). Delete the layer mask by right clicking it in the layers panel and choose Delete Layer Mask. Then after you have edited the path, turn it into a selection again, and add another layer mask.
The moral to this story is to make sure your path is right before you turn it into a selection and apply the layer mask. Examine it closely by zooming in.
It would be great if GIMP had live vector masks you could edit (like Photoshop), but it doesn't have this feature yet. However, if the layer mask is not much wrong, you can also edit it directly by clicking on the layer mask thumbnail in the layers panel, and edit the mask using the Paint Brush tool to paint on the mask. Paint in black for full transparency, and white for full opacity.