Is it permissible, in Islamic law, for the bride to place the hymenal blood-stained cloth on her face on the morning after the wedding night for visitors to see, knowing that she is uncomfortable with it but her family insists on it to avoid gossip?

This is a bad custom that Islam rejects, and it must be abandoned because it violates its commands regarding purity and modesty, and it prohibits the disclosure of what transpires between spouses. To change these customs, first seek help from Allah, then gently and wisely explain the ruling of the matter to your family, and seek assistance from the wise people among your folk.