why can the Gadsden purchase be referred to as "conscience money"??

Look up the date and the date of the Mexican American war when the US took half of Mexico and made it New Mexico, Arizona, Southern California ....

See for example:

It was a perfect setup. By the treaty of Guadalupe-Hidalgo, signed February 2, 1848, at the close of the Mexican War, the Republic of Mexico was compelled to abandon its claim to Texas and to cede to the United States the territory now comprising most of New Mexico, Arizona, California, Colorado, Utah and Nevada. The territory ceded to the United States by Mexico constituted about 200,000 square miles or two-fifths of all her territory.

In return for this vast territory, the United States gave $15,000,000 and assumed responsibility for paying $3,000,000 in claims of American citizens against the Mexican Government. A large body of public opinion in the United States had opposed the war against Mexico and felt that the Southern republic had been treated badly. The territory desired by Gadsden and his group was then a sort of no man's land, experiencing frequent Indian raids. The United States wanted to make certain "boundary adjustments"; Mexico needed money and wanted a settlement of her Indian claims against the United States; and Gadsden and his friends wanted a route for their railroad. In 1852 Gadsden agreed to pay Santa Anna $10,000,000 for a strip of territory south of the Gila River and lying in what is now southwestern New Mexico and southern Arizona.

Many Americans were not especially proud of the Guadalupe-Hidalgo Treaty and considered the price of the Gadsden Purchase as "conscience money." The Gadsden Purchase has an area of 45,535 square miles and is almost as large as Pennsylvania. This tract of nearly 30,000,000 acres cost Uncle Sam about thirty-three cents an acre.

That is an excerpt from:

http://www.progress.org/gads.htm

The term "conscience money" is often used to describe payments made by one party to another as a way to appease guilt or moral obligation. In the case of the Gadsden Purchase, the term "conscience money" is sometimes applied due to the circumstances surrounding the acquisition.

To understand why it may be referred to as "conscience money," let's delve into the background. The Gadsden Purchase refers to the acquisition of a strip of land in present-day Arizona and New Mexico by the United States from Mexico in 1853. This land was sought by the U.S. government to facilitate the construction of a southern transcontinental railroad.

There are a few reasons why the Gadsden Purchase could be viewed as "conscience money":

1. Compensation for Past War Losses: The United States had Mexican-American War (1846-1848) as a result of which it obtained vast amounts of Mexican territory. The Gadsden Purchase, which consisted of 29,670 square miles, was another acquisition from Mexico. Therefore, some argue that this purchase was a form of financial reparations or compensation for the land taken during the war.

2. Alleviating Opposition to Slavery: The southern states, where slavery was prevalent, were eager to acquire land for the expansion of slavery. The Gadsden Purchase, with its strategic importance for the potential southern route of the transcontinental railroad, was seen as a way to appease the southern states and maintain unity in the nation. As a result, some perceived the payment for the land as an attempt to appease the "conscience" of the pro-slavery factions.

3. Addressing Border Disputes: The Gadsden Purchase also helped settle border disputes between the United States and Mexico. By officially purchasing this land, the United States aimed to establish clear and recognized borders, reducing tensions and potential conflicts between the two nations. The payment made for the land, therefore, can be seen as an act of goodwill and an attempt to mend past disagreements.

It's important to note that the term "conscience money" is subjective and not universally accepted. Different historians and scholars may have varying interpretations and viewpoints regarding the motivations and implications of the Gadsden Purchase.