Removing a file from the end user's device can be a tricky process, especially without resorting to methods like ActiveX that may limit compatibility with certain browsers.
Instead of deleting the file directly, you could set caching directives to prevent the browser from storing it in its cache and avoid writing it to disk (assuming the file is being fetched by the browser as part of loading the page).
One possible approach is:
Response.Cache.SetCacheability(HttpCacheability.NoCache);
Response.Cache.SetExpires(DateTime.Now.Subtract(new TimeSpan(1, 0, 0, 0));
Response.Cache.SetNoStore();
If there is a need beyond just preventing caching, using an ActiveX control might be necessary. However, deploying such a control should be done cautiously, following guidelines like those outlined in MSDN's documentation on Per-Site ActiveX Controls. Implementing an ActiveX control that allows file deletion across domains could pose serious risks both within an intranet and on the web.