Lulu here from the Shopify Support team. Thanks for reaching out to us here, and I'll be more than happy to help you out.
You should be able to change any shipping options in your admin by clicking Settings > Shipping. Once you locate the 1-2 day shipping, click Edit next to the shipping zone that contains the shipping rate that you want to delete:
We have this guide here too in our help center which breaks down the steps for you. That should get rid of that rate for you and it won't show up as an option anymore, however, if you are unable to follow these steps or cannot find the exact rate, then please share your store URL with me and I can take a closer look for you.
Lulu | Social Care @ Shopify
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