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

3 answers

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