Some people think that these rings increase the love between the spouses and have an effect on their relationship. This is an ignorant belief and is an attachment to something for which there is no basis in practical life and which does not make sense.
In principle there is nothing wrong with rings (i.e., they are permissible), unless they are accompanied by certain beliefs, as some people do when the man writes his name on the ring that he gives to his fianc'ee, and the woman writes her name on the ring that she gives to her fianc'ee, believing that this will guarantee the bonds between the spouses. In this case this engagement ring is banned, because it represents an attachment to something for which there is no basis in islamic laws and which does not make sense. Similarly it is not permissible for the man to put the ring on the woman's hand himself, because she is not yet his wife, so she is still a stranger (i.e., non-mahram) to him; she is not his wife until after the marriage contract is done. The engagement ring or wedding ring has a history of thousands of years old. Some people claim that the Pharaohs were the first to invent it long before the Greeks had any notion of it. Others say that it stems from an old custom still upheld by people. By this they are referring to tying the bride and the bridegroom together with chains and making him ride a horse, while dragging his bride behind him to the marital home, which might be a distance of two houses. Later, it became popular to wear a ring, instead of being tied with chains.
Wearing an engagement ring on the left finger is related to an old custom of the Greeks who believed that the circulation of blood by the aorta is done through this area.
It became apparent later that the British were also fond of wearing engagement rings; in fact, they regarded the habit as purely Christian.
Muslims adopted the idea of wearing the engagement ring without any obvious reason, and some consider removing it as a bad omen. This has no basis in Islam.