To make changes to your template, follow the "Template" link on the left-hand column of your Blogger home page and then the orange "Customize" button under the screenshot of your blog.
The Border Color, marked with a red box above, is where you can change that "pesky" frame color.
Remember, a Blogger template is just a great place to start. You can change colors and fonts, adjust widths and the overall layout. Make it your own!
Update: Based on comments from readers I have learned that not all Blogger templates allow you to change the frame on your images via the Blogger Template Designer. Kathryn of Kathryn's Quest found this link helpful. Beware, it does include editing HTML, but it's not difficult.