Step 1. Log into Blogger then click on "Design".
Step 2. Click on "Edit HTML"
Step 3. Press Ctrl+F to bring up your search field and type in .post img
Step 4. You should see a code that looks like this:
.post img, table.tr-caption-container {
padding: 4px;
border: 1px solid #cccccc;
Step 5. Change the border 1px to 0px.
Step 6. Preview your blog then save.