When I search an external base via EndNote, all the hits are transferred to my EndNote library without asking for it. Can I avoid this?

Solution:

The transfer happens because you are in so-called «Integrated» mode.
Switch to «Online Search Mode» and the problem will disappear.

See more about you different modes under the description of library window toolbar
(These are the first three buttons that are relevant.))

 = Local Library Mode      = Online Search Mode  = Integrated

It can also be helpful to check the guide for searching via EndNote