I am using fedora and use "terminal" for command line activities.

When I list using ("ls"), Fedora displayed folder with different font color and sometimes highlighted the name. I found the setting in
/etc/DIR_COLORS and is able to change the settings and see the changes.

However, there is one type of folder that has font and background highlight very similar color. it is very hard to see the name and I couldn't find any setting that fix it (removing background color).

I noticed that the folder with this problem has "chmod 777" permission.

Can someone suggest what entry of the DIR_COLORS I should modify to change the background highlight to something else like underscore.

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The folders you are concerned about are symbolic links. In /etc/DIR_COLORS, look for something like this:
LINK 00;36 # symbolic link

Change the 00;36 to the colors you prefer.

Actually the attached image does not match the spell:
It is not clear to what directory this comment is related... actually there is no directory in the list shown! I can only guess you refer to directories that have all permission bits set, like those ones stored on a FAT or NTFS filesystems, e.g.
The reason for the green background is due to the bit "writable by others" or "o+w" and the flag which controls this behaviour is OTHER_WRITABLE. However this control is not set in /etc/DIR_COLORS but you can always add it. For example, if you want them in blue text and underlined:
I really don't know where actually these and other settings are stored, but the dircolors man page clearly states that if no file is specified as argument "a precompiled database is used". Maybe this database is stored in the binary executable of the dircolors command itself, but it can always be overridden by settings in /etc/DIR_COLORS or better by $HOME/.dir_colors (for your own personal settings).

Finally, you can see the complete set of colorized items using:
Hope this helps.