Slogans were painted on the monument at White Brae, Ligoniel, on the outskirts of north Belfast and two wreaths were removed.
The monument is a tribute to teenage brothers John and Joseph McCaig, and their colleague Dougald McCaughey, 23.
The off-duty fusiliers were shot dead at the site by the IRA in March 1971.
James Wright, chairman of Oldpark and Cavehill branch of the Royal British Legion, said: "Just like the cowards who in the dead of night murdered John, Joe and Dougald, these lowlife cowards cannot show their faces, they have to carry out their attacks under the cover of darkness.
"As a branch we will not be deterred in ensuring that the murder of these young soldiers who were off-duty and out socialising in Belfast will never be forgotten."
Sinn FÃ©in councillor for north Belfast, Gerry McCabe, also condemned the latest incident.
"The ongoing attacks on this memorial must stop.  They have gone on too long," he said.
"The actions of those involved in this are not representative of the people of this community and whoever is behind this should question what they are achieving."

The senator from South Carolina told CBS This Morning that he would make an official announcement on 1 June in his home town of Central.
But when asked why he was considering it, he said "I'm running" because "the world is falling apart" and he would make the best commander-in-chief.
He becomes the seventh leading Republican to join a crowded field.
Mr Graham has been a fierce critic of President Barack Obama's foreign policy, particularly in the Middle East.
He wants US ground troops to be sent into Iraq and Syria to combat Islamic State, to prevent terror attacks in the US.
Lindsey Graham tried to be coy about whether he was going to run for president, but his decision is clear - he's in. That makes four members of the US Senate - 9% of all Republican senators in office in 2014 - now running.
A foreign policy hawk in the mould of Senator John McCain of Arizona, he is likely to make national security the central theme of his campaign. If polls are to be trusted, that may play well with Republican audience.
He is still a long-shot, however, given that his past efforts at co-operation with Democrats and support of sweeping immigration reform put him out of step with many Republican primary voters.
The mere fact that he's in a position to run for president now, however - given that just a few years ago he was seen as a prime target for a grassroots Tea Party primary challenger - is an impressive political achievement.
When asked by CBS whether he thought the Republican field was weak, he revealed his intention to run himself.
"I'm running because of what you see on television, I'm running because I think the world is falling apart, I've been more right than wrong on foreign policy," he said.
"It's not the fault of others, or their lack of this or that that makes me want to run, it's my ability in my own mind to be a good commander-in-chief and to make Washington work."
Meet the 2016 hopefuls
A memorial to three Scottish soldiers who were murdered by the IRA has been attacked for a 19th time, the Royal British Legion has said.
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Senator Lindsey Graham, the Republican foreign policy hawk, has confirmed that he will run for US president in 2016.