To get "no border" when making block with background I use i3blocks
in file ~/.config/i3blocks/config
above any [BLOCK] put:
separator_block_width=-16
markup=pango
example:
separator_block_width=-16
markup=pango
[SOME_BLOCK]
full_text=<span bgcolor='#ff0000' >LOL</span>
some blocks are too short then - so I put spaces at the end of full_text
(after </span>
!)
value -16
probably You need to corelate with i3bar font size (bar
section in ~/.config/i3/config )
You can also use normal i3status and then put two needed lines in every block so it could be "borderless"