First, copy the image to a new layer and use your favorite tool to select the stars.

Then expand the selection, to include some of the background around the stars, and feather a bit.

Set the blend mode to darken.

Use Ctrl-H to toggle off the "marching ants".

Now use the Move Tool to move the selection in the direction of the elongation one or two pixels.

Deselect the stars, and flatten the image.

Finally, select the stars again, without expanding the selection, and brighten the center of the stars to match the original image.

Final Note:  If a one pixel move is too much, double the image size, fix the stars and then reduce the image back to the original size.