It's easier to evaluate pearls that have been photographed against a white or light neutral background. However, I think I am reading the word "Monet" on the back of the clasp. Monet is a brand of fashion jewelry. If you have a magnifier could you check this?
Try rubbing 2 of the pearls together gently. Are they gritty feeling, or do the just glide smoothly? Real pearls will feel a bit gritty while imitation pearl coating will just glide.
Also:
• The knots are a bit large for the size of the pearls. Imitation pearls often have larger drill holes than real pearls. Larger drill holes require thicker thread and thus larger knots.
• I see what look like characteristics of imitation pearl coating near some of the drill holes
• They are very uniform and do not have much luster, and no overtones.
I think they are imitation, but do check the clasp and rub the pearls together.
Edited to add:
I searched for Monet pearl necklaces on eBay and found one whose clasp looks the same:
Monet necklace with same clasp on eBay
So that's it-- it's imitation.
But it can still be sentimental!