The ban as currently phrased forbids the use of these terms within both budget documents, and supporting documents submitted with the budget, including research abstracts and study proposals. That's a fairly significant footprint.
As far as why the CDC would be concerned with transgender persons, well, there are medical implications and impacts out there that are relevant to the transgender community. Under the CDC, for example, National Center for HIV/AIDS, Viral Hepatitis, STD, and TB Prevention is working on ways to prevent HIV among transgender people and reduce health disparities. Transwomen have an HIV infection rate about four times higher than the general population within the USA. In a recent WHO report, there was a meta-analysis demonstrating that a transgender woman was 49 times as likely to be living with HIV [than the general population] in 15 countries in which data was looked at and analyzed. Access to care and treatment management for medical issues the transgender community is prone to have also falls under the CDC.