Improving Confidence in Veterans' Care Act This bill prescribes oversight requirements for the Department of Veterans Affairs (VA) regarding health care professionals at VA medical centers. Specifically, the bill requires the VA to ensure each VA medical center consistently compiles, verifies, and reviews specified documentation for each VA health care professional (including contractors). The VA shall ensure that specified health care professionals hold an active Drug Enforcement Administration registration. Each VA medical center must implement (1) monitoring of the performance and quality of the health care delivered by each health care professional at the center, and (2) reviews of such care if an individual notifies the VA of any potential concerns relating to a failure to meet generally accepted standards of clinical practice. The bill imposes notification requirements in situations where the VA substantiates a concern relating to the clinical competency of, or quality of care delivered by, a current or former VA health care professional. The VA is prohibited from entering into a settlement agreement relating to an adverse action against a VA health care professional if such agreement includes terms that require the VA to conceal certain information from the employee's personnel file. Such prohibition does not apply to adverse actions determined to be prohibited personnel practices. The VA must provide mandatory training, at least biannually, to employees of each medical center who are responsible for specified tasks (e.g., those who are responsible for compiling, validating, or reviewing the credentials of VA health care professionals).