For convenience, gtk_spell_checker_new() is created as GInitiallyUnowned and gtk_spell_checker_attach() will sink the floating reference. gtk_spell_checker_attach() also connects the destroy signal of the passed-in GObject to g_object_unref() the GtkSpellChecker, so in the most common use-case, you need not worry about cleaning it up. However, if you want to detach and later reattach the GtkSpellChecker to a (possibly different) GtkTextView, you must get a pointer to it with gtk_spell_checker_get_from_text_view(), call g_object_ref() on the resulting pointer, call gtk_spell_checker_detach() on it, call gtk_spell_checker_attach() with the new GtkTextView, and finally call g_object_unref() to release the reference that you took at the beginning, like this:

GtkTextView* view = gtk_text_view_new ();
GtkSpellChecker* spell = gtk_spell_checker_new ();
gtk_spell_checker_set_language (spell, "en_US", NULL);
gtk_spell_checker_attach (GTK_TEXT_VIEW (view));
/* ... */
// Detach
g_object_ref (spell);
gtk_spell_checker_detach (spell);
/* ... */
// Reattach
gtk_spell_checker_attach (spell, GTK_TEXT_VIEW (view));
g_object_unref (spell);

Alternatively, you can sink the GtkSpellChecker immediately upon construction with g_object_ref_sink(), in which case you will retain the ownership of the GtkSpellChecker throughout the lifetime of the program, and you must remember to call g_object_unref() when you don't need it any more, like this:

GtkTextView* view = gtk_text_view_new ();
GtkSpellChecker* spell = gtk_spell_checker_new ();
g_object_ref_sink (spell);
gtk_spell_checker_set_language (spell, "en_US", NULL);
gtk_spell_checker_attach (GTK_TEXT_VIEW (view));
/* ... */
// Detach
gtk_spell_checker_detach (spell);
/* ... */
// Reattach
gtk_spell_checker_attach (spell, GTK_TEXT_VIEW (view));
/* ... */
// End of life time
g_object_unref (spell);