When we speak or write in English, both “Mrs Pandelidi” and “Mrs Pandelidis” are correct.
When we speak or write in Greek however, the correct form is only “η κυρία Παντελίδη”, due to the conjugating rules:
η κυρία Παντελίδη
της κυρίας Παντελίδη
την κυρία Παντελίδη
ο κύριος Παντελίδης
του κυρίου Παντελίδη
τον κύριο Παντελίδη
You will notice that for the female we always use the form “Παντελίδη”. This comes from the male genitive because, in the older days, the women had less social status and they always belonged to a male, either father or husband.
A Greek woman that lives abroad may decide to use the correct Greek form which is “Mrs Pandelidi”. However this will create confusion and legal problems, since she will have a different last name from her husband/father (“Mr Pandelidis”). So the common practice is to adopt the same name as the husband/father (“Mr Pandelidis”).