The union will have a mandate to go on strike again within six months if it looks like the cuts are being reintroduced or the budget is not going to pass.
However, the SNP group's size means it is unlikely to fail.
GCC previously said no teachers in permanent jobs would be made redundant and that savings would come from not filling vacant posts or reducing staff on temporary contracts.
The local authority said it needed to look at every option to make savings, as the education budget covers more than half the local authority's direct expenditure
Last year the Education Secretary Jenny Gilruth revealed she had not allowed the £145.5m which was set aside to maintain teacher numbers to be paid to councils.
This was because some - including Glasgow - had cut teacher numbers.
However, in December Cosla and the Scottish government signed an official agreement to maintain teacher numbers and freeze learning hours.
Parents had argued the proposed cuts would disproportionately impact children with additional support needs and those living in poverty.
The council has been approached for comment.