The phrase "to limit the evidence" means to reduce or control the amount or types of information available to support or prove something. Full definition
As an example, teacher residency programs have captured interest nationally, but we have only limited evidence of their effectiveness compared to more traditional teacher - preparation programs. (educationnext.org)
The result: a person's automatic perceptions come to conclusions based on limited evidence and her intuitive beliefs. (baylor.edu)
So we need to be careful to not draw more conclusions than can be justified from the more limited evidence from the early 20th century. (skepticalscience.com)