After clicking the "Edit this issue" link, a user with sufficient access rights and proper screen setup can edit Resolution field. The problem is that the dropdown list of the field does not contain the "None" value, which would allow for clearing resolution. Currently the only workaround is to run a transition, where a post-function is defined, which clears resolution. It is interesting that in the post-function setup screen, the dropdown list of resolution values contains the "None" value.