It follows a successful online fundraiser set up by the trust, which hit its target of £2,000 after less than one day, to replace the plaque on Leeds Bridge and improve security.
A blue plaque, which comemmorates David Oluwale - a British Nigerian man whose death led to the historic prosecution of two police officers - had been unveiled on Monday, before being stolen that same evening.
The temporary plaque was put in place after the first plaque, but on Thursday morning, this had also been destroyed.
But Leeds Civic Trust director Martin Hamilton has said they won't be cowed by the racists into giving up, and has thanked the Leeds public for its generousity in meeting the fundraising target.
He said: "It's fantsastic. Normally it takes longer than a day to get that response. It's not just a couple of people giving large amounts of money either, there are 151 different people chipping in, and that shows the strength of feeling.
"We are not going to step back on this. The reasons why we put the plaque up have not changed, and putting something in place on a temporary basis until the plaque has been found or until we get a new one, is the right thing to do. I think it is a real shame that someone has chosen to damage it.
"But we can't just say 'fine, we'll give up then'."
He added that the money will go towards getting a new plaque, but that the trust was looking at extra security, which could include a new CCTV camera.
"After a lot of thought and discussion, it was decided that that was the right place to put it. Obviously it is within arm's reach. It is quite low down. We will also look at ways where we can attach it that would make it much harder to remove.
"There are a variety of things we will be able to do. I don't feel like we should be changing tack and putting the plaque somewhere else, just because of what's happened. The place on the bridge overlooking the River Aire is the right place to have it."
A spokesperson for West Yorkshire Police said: "We have been made aware today that a laminated image of the David Oluwale plaque, which was put in place on Leeds Bridge at the site of the original plaque, has been damaged overnight.
"We are treating this as a further hate crime, given the circumstances, and are carrying out enquiries to identify the person responsible.
"Detectives are also continuing to carry out enquiries into the theft of the original plaque, which was taken some time between 9.30pm and 9.55pm on Monday, April 25.
"We are still keen to hear from anyone who was in the area of the bridge on that night, particularly if they were taking photographs of the plaque that could assist in further narrowing down the timeframe in which it was taken or help to identify anyone acting suspiciously in the area around that time."