The filter ‘date_i18n’ can be used to reformat the date being returned by the function of the same name (used to format the date from feed data). The date’s timestamp is passed as the third parameter so use of strtotime()
is not necessary. This filter will affect much more date display than that of the widget, so a filter hook should only be added in the correct context. The ‘widget_title’ filter fires before ‘date_i18n’, so can be used to only add in the right context. Only add a callback to ‘date_i18n’ when the passed widget title matches the title of your RSS widget instance.
I don’t see an easy way to remove the callback again after its use in no longer needed. If there is no subsequent date output after the widget this may not be an issue. If another widget occurs after RSS, maybe ‘widget_title’ can be used again to remove as well.
Unless you already have a child theme or plugin to contain custom code, you should create one or the other (plugins are easier to create). It’s best to avoid editing code files, especially WP core files. Add code to hook the previously mentioned filters with callbacks to effect change as I’ve described.