The artwork on the 'International Wall' relating to the Home Rule crisis in 1912 was defaced with white paint.
The mural, partly, replaced an image of Kieran Nugent who started the IRA blanket protest in the Maze H Blocks.
The work was painted as part of a display to mark the centenary of the Easter Rising and the events running up to it.
Carson led the resistance to home rule and was the first to sign the Ulster Covenant in 1912.
He also helped establish the UVF.
The protest was held at midday Friday at the mural by the Belfast 32 County Sovereignty Movement which said it was an "insult to the people of the Falls Road".
In a statement it said: "The Belfast 32 County Sovereignty Movement would like to make clear that we encourage and support all genuine Republicans in the upcoming Easter events that will be remember and celebrating the Centenary of the Rising, may it be flags, marches, talks, murals etc.
"We do not support the revisionist agenda by some in our community, our mural was paid for by our members and we were never consulted on the removal of our mural, and to replace the mural of Kieran Nugent with Carson was an insult to the people of the Falls Road."
Nugent, the first IRA man on the blanket protest in the H-Blocks, died in 2000. When warders asked him to wear prison uniform, he replied: "You'll have to nail it to my back."
The Carson mural depicts the unionist leader with an outstretched arm.
It also shows armed members of the original UVF militia, as well as a convoy of cars travelling along a dark road depicting the Larne gunrunning operation.