diff --git a/kitty/mouse.c b/kitty/mouse.c
index cbe6a5919..706a1e52f 100644
--- a/kitty/mouse.c
+++ b/kitty/mouse.c
@@ -902,6 +902,14 @@ mouse_event(const int button, int modifiers, int action) {
         }
     }
     w = window_for_event(&window_idx, &in_tab_bar);
+    if (global_state.mouse_hover_in_window) {
+        Window *old_window = window_for_id(global_state.mouse_hover_in_window);
+        if (old_window && old_window != w) {
+            global_state.mouse_hover_in_window = 0;
+            screen_mark_url(old_window->render_data.screen, 0, 0, 0, 0);
+        }
+    }
+
     if (in_tab_bar) {
         mouse_cursor_shape = POINTER_POINTER;
         handle_tab_bar_mouse(button, modifiers, action);
diff --git a/kitty/shaders.c b/kitty/shaders.c
index 1d1568f40..0cdb1101e 100644
--- a/kitty/shaders.c
+++ b/kitty/shaders.c
@@ -814,7 +814,7 @@ render_a_bar(const UIRenderData *ui, WindowBarData *bar, PyObject *title, bool a
 
 static bool
 has_hyperlink_target(OSWindow *os_window, Window *w, Screen *screen) {
-    return OPT(show_hyperlink_targets) && screen->current_hyperlink_under_mouse.id && w && !is_mouse_hidden(os_window);
+    return OPT(show_hyperlink_targets) && screen->current_hyperlink_under_mouse.id && w && !is_mouse_hidden(os_window) && global_state.mouse_hover_in_window == w->id;
 }
 
 static void