Enclosing your variable with double quotes will definitely not give the expected result. It will simply treat {{res.website}}
as a string and compare it with none
.
Simply write:
{% if res.website != "none" %}
<img src="{{ asset('bundles/foo/images/web-icon.png') }}" />
{% endif %}
If you still have an error, make sure res
is a valid variable in the current scope.