Zencastr saves local backups of each participant's track while you record. The browsers grant a quota of disk space for application to save to. The amount made available is around 10 - 20% of the total local disk space available on the participants hard drive.
The quota available for local backups is below the recommended level.
If the participant has less than 20GB of free disk space on their computer, then the browsers can't grant the recommended 2GB of disk space. Clearing off more disk space and then restarting the browser will help solve this issue.
If the problem persists or or the participant has more than 20GB free and is still seeing this warning, then they may have already used the quota in past Zencatr recordings. They can clear out any past backups by following the instructions here: How do I delete past Zencastr recordings?