Is it permissible to set a specific amount for contributing to the building of a mosque with a promise to gift an 'Umrah to one of the contributors, or is that considered gambling?

Your effort in building the mosque is a righteous deed for which you will be rewarded, based on the Almighty's saying: (Indeed, only those who believe in Allah and the Last Day shall maintain the mosques of Allah) and the Prophet's (peace be upon him) saying: (Whoever builds a mosque for Allah, even if it is as small as a bird's nest, or smaller, Allah will build for him a house in Paradise).

However, the method of collecting donations by linking it to a raffle for an 'Umrah trip is forbidden, because it falls under the category of gambling and Maysir, which Allah Almighty has prohibited. Allah Almighty says: (O you who have believed, indeed, intoxicants, gambling, [sacrificing on] stone altars [to other than Allah], and divining arrows are but defilement from the work of Satan, so avoid it that you may succeed).

Moreover, the desire of the donor to win an 'Umrah trip through donation makes the charity a type of compensation, and the Prophet (peace be upon him) forbade taking back charity.

Therefore, this method of collecting donations should be abandoned, and it is sufficient to encourage people by reminding them of the reward in the afterlife and what Allah has promised to those who spend, such as building a house in Paradise for whoever builds a mosque for Allah Almighty.