Smudge on rear lens element

I recently purchased a Pentax 50mm f1.2 lens (K version, with the newer font on front) on the 'bay. When I first looked at photos of the lens, there appeared to be what I thought were cleaning or coating marks on the front element. I asked the seller, who said that he did clean the lens before listing it, but then sent me other photos of the lens' front element to show that the cleaning marks had "faded away" from when he first cleaned. The photos in the listing didn't show anything apparently wrong with the rear element.

When I received the lens, I noticed these markings on the outer edge of the rear element in the photo below. I believe they are marks on the coating from the seller cleaning the lens, but I am wondering if they will have any significant effect on photos made with the lens. If things like contrast and flare are affected, could they just be mitigated with something like a lens hood? Is there a way to remove these markings with more careful cleaning by a professional? Thanks in advance, and I apologize if this has already been talked about in a previous thread - I did some searching but didn't find anything that matched my issue.

It does appear to be from cleaning, either incompletely or residue from a liquid cleaner. Doubtful that it will affect image quality in a noticeable way except perhaps at the widest aperture. It shouldn’t be difficult to clean with a coated lens cleaning solution and a fine lens cloth or tissue. Add the solution to the cloth, not the lens, and wipe the element in an outward circular motion. Given that the smudge is on the edge, you may only need to clean the outside of the element. Smudges like that can happen when the grease from a fingerprint is not removed completely.

Interestingly, I also have what appear to be scratches along the outer part of the rear lens like Aviv's, or maybe a separation inside. Is there a way to test it with a shot that would show if there are any actual effects in a photo? A blue shy? White wall?

Finn lyle said:

It does appear to be from cleaning, either incompletely or residue from a liquid cleaner. Doubtful that it will affect image quality in a noticeable way except perhaps at the widest aperture. It shouldn’t be difficult to clean with a coated lens cleaning solution and a fine lens cloth or tissue. Add the solution to the cloth, not the lens, and wipe the element in an outward circular motion. Given that the smudge is on the edge, you may only need to clean the outside of the element. Smudges like that can happen when the grease from a fingerprint is not removed completely.

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Thanks for the advice - I'll probably give it a shot with a coated lens cleaner then. I got this lens primarily with the hopes of using it in low light at 1.2, so I just want to make sure that I can use it without issue at that aperture.

Alan Edward Klein said:

Is there a way to test it with a shot that would show if there are any actual effects in a photo? A blue shy? White wall?

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What is a blue shy? I've never seen one.
Photograph a solid color or two or three frames light, medium, dark, with the sun at a 45° angle to the lens without the sun being in the frame. Haze, fine scratches will show up more as flare or reduced contrast and be more appearant with the sun in front of you.