Your HomeRunner site does not show a lower price or a strike-through price for a stay.
Why this happens. HomeRunner prices each stay by asking Hostaway for a quote, and Hostaway returns the nightly rate and fees for those dates. This is how the Hostaway connection works today. It is not a sync delay or a website setting.
What you can do. Create the coupon in Hostaway, then have your guests enter the code in the coupon field on the booking widget or at checkout. If the coupon field is not visible on your site’s booking widget, contact support to enable it.
If you want a lower price or strike-through display on your Hostaway-connected site, contact support to discuss options.