I haven't used filtering in exported HTML5 maps for a little while but when I went to do this today I discovered that the map is displayed in its filtered state as you would expect but with a warning that a filter has been applied. If the end user clicks on this the filter is removed, but unless I am missing something there doesn't seem to be any way you can return the map back to its filtered state.
This approach is very undesirable on at least two fronts. For example, you might want to publish only the filtered version of the map to HTML5 without making the full version available - and indeed you may also not want to indicate that the map is filtered. At the moment not only is the end user told the map is filtered but they also can see the full map just by clicking on the filter warning.
On the other hand you might want to provide both the filtered and unfiltered versions of the map in the HTML5 export so the end user can switch between them. Currently however, it seems you can go only from the filtered to the unfiltered view and not back the other way.
The HTML5 export menu should be changed so that when you want to export a filtered map you are given the option to indicate whether an indication should be added to state whether the map is filtered or not. If you elect to add such an indication you should then also be able to decide whether the end user has the option to switch between the filtered and unfiltered views of the map.