Hi Newman This is an informal word, describing a number you don't want to count. It's a bit like 'yet another'. Older ladies tend to be a little bit 'sensitive' about people knowing their age, (hence your expression, 'of a certain age'). The birthday card is using this as a joke, a play on the coyness of revealing a lady's age. Unpteenth is often used in sentences like this: "This is the umpteenth time you've interrupted me!" "She dropped her toy from the pram for the umpteenth time." "You must be the umpteenth person to have asked me that question!"

for someone age undisclosed