Can you please remove from the web.config file the following lines (under the system.webserver tag)?
<add name="GeminiApiAdmin" verb="" path="api/Admin.ashx" type="CounterSoft.Gemini.Web.Api.AdminRestHandler, CounterSoft.Gemini.Web"/>
<add name="GeminiApiAlerts" verb="" path="api/Alerts.ashx" type="CounterSoft.Gemini.Web.Api.AlertsRestHandler, CounterSoft.Gemini.Web"/>
<add name="GeminiApiCustomFields" verb="" path="api/CustomFields.ashx" type="CounterSoft.Gemini.Web.Api.CustomFieldsRestHandler, CounterSoft.Gemini.Web"/>
<add name="GeminiApiGroups" verb="" path="api/Groups.ashx" type="CounterSoft.Gemini.Web.Api.GroupsRestHandler, CounterSoft.Gemini.Web"/>
<add name="GeminiApiIssues" verb="" path="api/Issues.ashx" type="CounterSoft.Gemini.Web.Api.IssuesRestHandler, CounterSoft.Gemini.Web"/>
<add name="GeminiApiProjects" verb="" path="api/Projects.ashx" type="CounterSoft.Gemini.Web.Api.ProjectsRestHandler, CounterSoft.Gemini.Web"/>
<add name="GeminiApiUsers" verb="*" path="api/Users.ashx" type="CounterSoft.Gemini.Web.Api.UsersRestHandler, CounterSoft.Gemini.Web"/>
This should do the trick.