Well, there's not much to refactor, really. It's readable, and I assume it works as expected. But here are a couple of ideas anyway
Simplest one: Using else if
just to avoid extra identation
linkStyle: ->
if @model.get 'published'
'published'
else if @model.get 'started'
'started'
else
'default'
Postfixing the conditions plus explicit returns:
linkStyle: ->
return 'published' if @model.get 'published'
return 'started' if @model.get 'started'
'default' # implicit return
Avoiding duplicate strings:
linkStyle: ->
for value in ['published', 'started']
return value if @model.get value
'default'
And so on...