close is not the same as back, they are completely different actions.
With close, your users will understand they're closing the active element (eg, your modal). With back, they may understand they will go to the page previous to the search OR that there are previous items (such as products).
The above being said, the additional close button might not be STRICTLY needed, but it's highly recommended. Also, you should be careful to have a label for screen readers, see for example Bootstrap's Close Icon recommendations
Use a generic close icon for dismissing content like modals and alerts. Be sure to include text for screen readers, as we’ve done with aria-label.
Same goes for Zurb's Foundation close icon
A close button is a element with the class .close-button. We
use the multiplication symbol (×) as the X icon. This icon is
wrapped in a with the attribute aria-hidden="true", so screen
readers don't read the X icon.
The button is also labeled with aria-label to clarify what the
button's purpose is.
As you may see, they don't say anything about visible labels, but even then they preserve the aria-label
Depending on the content, you may want an acknowledgement rather than a close button. For example, if your content is a message that you want your users to read, it's better to offer a button with an acknowledgement such as OK, got it or Yes, I understand rather than close
Also, if these modals are just dialog boxes, a close icon is enough
Unless you have spacing constraints, use the button, but make sure to consider what type of message are you using in your modal