If you're cloning with http or https protocol, then you may be able to write the URL as:
Replace username with the evaluated value of GIT_USERNAME and replace password with the evaluated value of GIT_PASSWORD.
If you're cloning with ssh protocol, then you need a private key / public key pair, not GIT_PASSWORD.
The GIT_USERNAME and GIT_PASSWORD environment variables are not read by the git plugin or the git client plugin as far as I can tell. Thus, I assume your jobs were expanding their values and using them in the authentication steps.
They could also have been used as input to a git credential helper, though that would need to be configured on every agent in the home directory of the user running the agent. I recommend against that technique because it increases the work you must do to maintain your agents.
While those are my guesses, my recommendation is that you switch to use the Jenkins credentials system to record your git user name and password inside Jenkins, then modify your job definition to use those recorded credentials. That avoids displaying username and password in job logs, and significantly reduces the risk of someone misusing your username/password combination.
Mark WAite