It’s really hard to determine what is going on but here’s what I can tell you…
Connections does not integrate with the core WP search so using the site search should not ever return anything from the directory. I’m assuming you are using a plugin or something which enhances the core WP search???
The error message you are seeing, that is in Connections but does not seem to be coming from Connections… I say this because it is not quite right. It’s missing the inline styling and the punctuation is wrong. Was Connections altered in any way?