The phrase "damage trust" is correct and usable in written English. It can be used generally in a sentence to describe when someone has done something that has reduced another person's trust in them, or hurt the trust within a relationship. For example: "John's dishonesty really damaged trust in our relationship.".
Lack of regulation may also damage trust in mobile money.
My fear is that this will damage trust between the government and junior doctors still further.
They said the database was intrusive and would damage trust built up between parents and tutors.
"Some of our future games may have in-app purchase in, but we're only going to do it in a way that doesn't damage trust with parents.
First was the financial crisis, which damaged trust in banks.
Much work remains to be done to restore damaged trust.
He damaged trust in politics: he pledged to cut migration to the "tens of thousands".
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com