Can you please shre your URL so that I can check, because by default its shown in footer in middle of the footer. So please share URL so that I will let you know exactly.
Dallas here from the Shopify Social Care Team.
Based on what you're showing I'm thinking that you have an app attached to your store for this search feature. Is that right? This search bar icon isn't native with the Jumpstart theme in Shopify, that's why I'm thinking this.
You can take a look at your apps by going to your Shopify Store Admin and Clicking on Apps on the left-hand side. If you look in there can you see anything that could be called something like Instant Search, Store Search, Smart Search or anything?
If you do then the search icon would be related to that. If you reach out to their support they might be able to help you with the location of the search icon. That would only be if you want to keep it and just move it out from under the messenger icon. However, with things like this, it's not guaranteed that they'll be able to fix that for you.
However, if you just want to get rid of it then you can just delete it. One more thing I'll add, however, is if you've added any code into the theme liquid of you're store then it might still show up. In that case, you'd have to be sure to remove that code. However, you can try the above steps first.
Let me know how this works for you.
Ah, you do have an app like that. In that case, you'll certainly want to talk with the app developers to see if that could be it. If it's not we can work on verifying your account and I can take a closer look for you to see if we can find some other options.
However, talk with the app team first and we can go from there.