Currently there's:

void vte_terminal_set_color_background(VteTerminal *terminal,
                                       const GdkColor *background);
void vte_terminal_set_background_image(VteTerminal *terminal, GdkPixbuf *image);
void vte_terminal_set_background_image_file(VteTerminal *terminal,
                                            const char *path);
void vte_terminal_set_background_tint_color(VteTerminal *terminal,
                                            const GdkColor *color);
void vte_terminal_set_background_saturation(VteTerminal *terminal,
                                            double saturation);
void vte_terminal_set_background_transparent(VteTerminal *terminal,
                                             gboolean transparent);
void vte_terminal_set_opacity(VteTerminal *terminal, guint16 opacity);

The tint_color is not needed.  color_background should affect the tint color too.

Opacity and saturation are the same thing.  No need for two.  We may want to add a new boolean to turn true transparency on/off.

Note that currently opacity doesn't work if a background image is set.  We do saturation instead.