It seems like it is 'within' the eyeglass lens itself - What could it be?

[Pinetops]

There is a red spot on my new eyeglasses which can't be removed by cleaning- it is visible in direct light

[Reidsville]

If the red spot can not be cleaned as you say,likely is under the coatings applied to the lens, and it appeared for some reason during manufacture. Anyway it would be better for you to notice the spot on buying the glasses, to avoid this trouble.Unfortunately, there is not an eyeglass lens repair kit that can improve a defect of the lens like this.

[Corsica]

You can go back to the store where you bought the glasses. Being new glasses, likely that you will be able to use the warranty agreement, and they change your lens, if you don't have any responsibility for the occurrence of the spot or scratches (I mean you have not damaged the lens).