Hello,

01. Your issue has been resolved. You are using the custom header of your site. I have edited the header and in the mobile menu disable the options.

You can check the custom header for a separate page and edit it.
https://xtemos.com/docs-topic/how-to-set-different-header-for-specific-page/
https://xtemos.com/docs-topic/options-for-pages/

02. Navigate to WoodMart > Header builder > edit default header (highlighted star icon) or you can go through the admin bar directly https://prnt.sc/Ct9ehRDvvDV9. Switch to mobile Header > Configure logo Settings and change the logo.

Screenshot for clarification:
https://ibb.co/8b9Ptn1

Best Regards.