$('.actionButton.single-pet').attr("style", "display: inline !important");
Sets CSS to display: inline !important;. display: inline is the default property for display. You need !important again to override the previous !important.
Note that !important shouldn’t be used often. Read the accepted answer at How to override !important? for more details.
UPDATE: We can’t use .css() here as it does not support !important. http://bugs.jquery.com/ticket/11173 for more details; appears to be a bug.