Reading of oxymeter. Of her skin.

Since past 2-3 months...my grandmother oxygen is not stable on oxymeter...it never remains on one number...its goes to 95 and then comes to 77 also times...but she doesn't have any respiratory issue...she is saying...she is feeling absolutely fyn...two doctor advised to change oxymeter also...and we changed oxymeter...but still her values are approx always wrong...last nyt her oxygen was showing 77 and she was not having any problem...she is on supplemental oxygen ...and all the oxymeter work fyn with us ...but not with her...i have one doubt...is it because of her skin...as due to old age her fingers have many wrinkles and skin also has changed a lot ...please doctor's help us ..below attached is her last year discharge summary...she is feeling all good...but her oxygen levels are not understandable