How can I hook into the wp_mail function used by BackWPup?

Looking at the source of the wp_mail() function, there’s a filter right near the top:

$atts = apply_filters( 
    'wp_mail', 
    compact( 'to', 'subject', 'message', 'headers', 'attachments' )
);
// Expanded for clarity.

(Aside: compact() is a PHP function that creates an array from a set of arguments. In this case, it’s making an array of the $to, $subject, $message, $headers, and $attachments parameters passed to wp_mail().)

…and then a little further on:

if ( isset( $atts['subject'] ) ) {
    $subject = $atts['subject'];
}

So yes, you can filter the message. Something like this should do the trick:

add_filter( 'wp_mail', 'wpse343761_filter_message' );
function wpse343761_filter_message( $atts ) {
    if ( ! empty( $atts['message'] ) ) {
        // If there's already a message, add to it.
        $atts['message'] .= 'Your additional text';
    } else {
        // If there's not a message set yet, set one.
        $atts['message'] = 'Your desired message';
    }
    return $atts;
}

Note: This code is untested.

Edit: In response to your update And, how can the “additional text message” be added to the beginning of the email?:

Change this line:

$atts['message'] .= 'Your additional text';

to:

$atts['message'] = 'Your additional text' . $atts['message'];

And to your strip_tags() usage question, you can do this:

$atts['message'] = strip_tags( $atts['message'] );

on the line before you return. (You can’t just use strip_tags( $atts['message'] ) because that doesn’t assign the stripped string to anything.)