Sauk warrior Black Hawk, the leader of a band of Sauks near Rock Island at Saukenuk, was always in opposition to ceding Native American lands to white settlers and their governments. Black Hawk supported the invalidity of the Treaty of St. Louis (1804) of both the Sauk and Fox nations negotiated with the then Indiana Territory Governor William Henry Harrison. The treaty ceded territory, including Black Hawk's birthplace Saukenuk, to the United States. The Sauk are a consensus decision making society. Their representatives exceeded the authorization of merely taking under consideration what terms the United States government might put forth, bring them back to reach a consensus and then return with their treaty terms. The lack of the tribe discussing the treaty prior to being made official made it invalid by Black Hawk and other members of the tribe. The representatives never had the tribal authorization to unilaterally cede its lands.  During the War of 1812 between the United Kingdom and the United States, Colonel Robert Dickson, an English fur trader, amassed a sizable force of Native Americans at Green Bay to assist the British in operations around the Great Lakes. Most of the warriors Dickson assembled were from the Potawatomi, Ho-Chunk, Kickapoo and Ottawa tribes. Dickson bestowed the rank of brevet Brigadier General on Black Hawk. He was given command of all Native Americans gathered at Green Bay, including the 200 Sauk warriors under Black Hawk's control. Black Hawk was then presented with a silk flag, a medal, and a written certificate of good behavior and alliance with the British. The certificate would be found 20 years later, after the Battle of Bad Axe, carefully preserved along with a flag similar to the one Dickson gave to Black Hawk.  During the 1812 war, Black Hawk and his warriors fought in several engagements with Henry Procter on the borders of Lake Erie. He returned home to Saukenuk to find his rival Keokuk had become the tribe's war chief. After the war ended, Black Hawk signed a peace treaty in May 1816 that re-affirmed the treaty of 1804, a provision Black Hawk later protested ignorance of.

Answer this question "Why did they believe the treaty was invalid?" by extracting the answer from the text above.
The treaty ceded territory, including Black Hawk's birthplace Saukenuk, to the United States.