Should the maid be confronted publicly with her theft, or is it sufficient to dismiss her without stating the reason upon seeing her steal something small?

If the maid is non-Muslim, do not keep her due to her untrustworthiness and the harms resulting from her presence. Her service must be terminated when the opportunity arises, unless there is a clear inclination towards Islam, along with extreme caution. If she is Muslim, the general principle is to offer her advice. If the stolen item is trivial and has not been repeated, then concealment and forgiveness are more appropriate.