The idea was to allow merchants to tag this specific product, so that it never shows up in the search (this is extra search parameter you can experience). As in Shopify sections do not talk to each other we had to add this tag all the time.
However, we realised this small annoyance in the stats, and due to the support it caused and how little the gift wrap feature was actually used, we decided to not automatically add this tag starting from the version 1.7.0 of the theme (the only downside is that for people using the gift wrap feature, this product may also appear in the search results).
For versions older than 1.7.0, please first take note that, except for the visual annoyance of having this search terms at the top, it does not cause any functional issue. We can however edit the code to remove this extra tag. As it implies editing the JS it’s a bit hard to explain it here, so just contact us at support and we’ll be glad to remove it for you :).