Thank you, Shaykh, for replying to my question, no. 2659074. You said that it depends on his intention.
1) I think I could not state my question right. I know that my husband's intention is the matter, but I wanted to ask: what if he did not intend anything; neither of placing my hand a with piece of cloth in between my hand and the Quran, nor of placing my hand directly without a piece of cloth? He did not say in his condition how I should place my hand, but he said, “If you do not place your hand on the Quran before March 22, you are divorced.” He did not think of how I should place my hand, with or without a piece of cloth, and in general people place their hand directly on the Quran without a piece of cloth, but he did not make it a condition that I place my hand on the Quran directly or indirectly with pieces of cloth in between my hand and the Quran, but he said, “If you do not place your hand on the Quran.” In this situation, will the condition be fulfilled by placing a piece of cloth between my hand and Quran, even without any excuse of not having performed ablution, or do I have to place my hand without a piece of cloth because he just said, “If you do not place your hand on the Quran,” and in general when people ask to place your hand on the Quran they mean placing the hand directly, without a piece of cloth when making any promise? I placed my hand on the Quran with a piece of cloth in between my hand and the Quran, but six days before the condition would end, a scholar siad to me, “Your husband said in his conditional statement, ‘Place your hand on the Quran,’ so you should place your hand directly with ablution, without a piece of cloth in between your hand and the Quran.”
2) Is touching the Quran with a piece of cloth without ablution a disputed matter? You said, “You can act according to the view of those who say that it is permissible to do that with a barrier, such as a cloth or the like, even if performing ablution is not difficult.”
I thank you for having answered on time, but could you clarify the question I wanted to ask? Thank you.

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

If the situation is as described and your husband did not hold any intention while saying “If you do not place your hand on the Quran before March 22, you are divorced,” then placing your hand on the Quran is achieved even if there is a barrier (the piece of cloth in this case). Hence, the condition has been fulfilled. What proves that placing the hand on the Quran does not require direct contact (of the hand with the Quran without a barrier) is the scholars' statement that the body parts of the prostration (which must be placed on the ground during prostration) do not have to come in direct contact with the ground in prostration.

The Hanbali scholar Al-Buhooti wrote, “The praying person is not obliged to make them ( the seven body parts of the prostration) touch the ground, and his prayer is valid if he prostrates while there is a barrier between the body parts and the ground. Al-Bukhaari said in his Saheeh, ‘Al-Hasan said, 'The people used to prostrate on the turban and cap.'’...” [Ar-Rawdh Al-Murbi’]

Hence, the most likely correct view in this regard is that placing your hand on the Quran with a barrier between them fulfills what your husband demanded because it is called placing, unless he intended otherwise.

If what he demanded was not fulfilled (if you did not place your hand on the Quran), then divorce takes effect according to the majority of the scholars, regardless of whether your husband intended to issue a divorce or merely to threaten and forbid you from doing something. Shaykhul-Islam Ibn Taymiyyah held that if the husband merely intends to threaten his wife, divorce does not take effect, and the husband is only required to offer an expiation if his oath was broken (i.e. he did not divorce his wife). The view of the majority of the scholars is the one adopted at Islamweb.

Regarding the ruling on touching the Quran with a barrier, the scholars held different opinions. Ibn Qudaamah wrote:

“They held different views regarding touching the Quran with a barrier such as a cover, a sleeve, or the like; the Maalikis and Shaafi‘is maintained that it is absolutely prohibited to touch the Quran while in a state of ritual impurity even if there is a barrier between the hand and the Quran. The correct view according to the Hanbalis is that it is allowed for the person in a state of ritual impurity to touch the Quran with a barrier that is not a part of it when it is sold, such as a bag or a sleeve, because the prohibition in this regard is regarding touching the Quran itself, and the person in this situation is touching the barrier and not the Quran. The same view was held by the Hanafis; they differentiated between a barrier that is attached to the Quran and the barrier that is separate from it. They held that it is prohibited to touch the Quran for the person in a state of ritual impurity except with a cover that is not attached (not sewn) to it or a bag. What is meant here by the cover that which is separated from the Quran such as the bag and the like, because if the barrier is attached to the Quran, it is considered part of it.” [Al-Mughni]

This is as far as the difference of opinion among scholars in this regard is concerned. It should be noted, though, that touching the Quran is different from placing the hand on it, and that placing the hand is achieved even if there is a barrier between the hand and the Quran.

Allah knows best.