We have previously stated in the answer to question no. 1695 that pigskin is najis (impure) and does not become taahir (pure) by means of tanning.
Simply touching something impure does not make the body impure, unless there is some wetness either in the impure substance or on the body.
Shaykh Ibn Jibreen said:
If the body or clothes are dry and touch something impure that is also dry, that does not matter, because the impurity is only transferred when it is wet. Fataawa Islamiyyah, 1/194
Based on this, the hand does not become impure simply by touching these gloves that are made of pigskin, unless the hand or the gloves are wet.
If the hands become impure by touching the pigskin when there is some wetness, then you have to wash your hands. It is sufficient to wash them once, because there is no command to wash something impure seven times, one of which is with dust or dirt, except in the case of impurity caused by a dog.
Some scholars likened the pig to the dog, so they said that one should wash seven times in the case of pig-related impurity, one of which should be with dust or dirt.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: “This is a weak analogy, because pigs are mentioned in the Qur’aan and they existed at the time of the Prophet (peace and blessings of Allaah be upon him), and there is no report which likens them to dogs. So the correct view is that pig-related impurity is like any other kind of impurity, and there is no need to wash seven times, one of which should be with dust or dirt.” Al-Sharh al-Mumti’, 1/356.
So the Muslim should strive to keep his body and clothes clean and pure, and avoid wearing these gloves that are made of pigskin, because that involves touching something impure and exposes his hands and clothes to the risk of becoming impure, which would affect the validity of his prayers. But if he needs to wear these gloves because he cannot find anything else, then it is permissible for him to wear them, so long as he is careful to avoid contaminating his body or clothes, and he hastens to wash off any impurity if he gets it on him, so that he does not transfer it anywhere else or forget to wash it off his hands or clothes.
There are permissible kinds of animal skins and leathers available which mean that there is no need for these impure types. We ask Allaah to help us to do that which He loves and which pleases Him. And Allaah knows best.