There was a question about the removal of DMF (similar to yours) from a reaction mixture 4 years ago at RG & there were several good answers:

https://www.researchgate.net/post/How_do_you_remove_DMF_without_using_a_vacuum_pump

Also there was a question about the removal of DMAP 4 years ago at RG:

https://www.researchgate.net/post/Is_anyone_familiar_with_the_removal_of_DMAP

Obviously DCC would have been converted to DCU by the end of reaction.

Since (DCC/DMAP) were used in small quantities, the work-up after finishing the esterification will remove what remained of them.

There was a question about the removal of DMF (similar to yours) from a reaction mixture 4 years ago at RG & there were several good answers:

https://www.researchgate.net/post/How_do_you_remove_DMF_without_using_a_vacuum_pump

Also there was a question about the removal of DMAP 4 years ago at RG:

https://www.researchgate.net/post/Is_anyone_familiar_with_the_removal_of_DMAP

Obviously DCC would have been converted to DCU by the end of reaction.

Since (DCC/DMAP) were used in small quantities, the work-up after finishing the esterification will remove what remained of them.

Usually, washing the organic phase 3-5 times with a satured solution of NaCl is a well-working work-up procedure able to remove DMF.

However, if you use large volume of DMF, it would be better to try to evaporate DMF as much as possible with rotavapor to few mL before proceding with work-up

I really wonder why some professors keep on recommending DCC as coupling reagent in e.g. amidation or esterification. There is 1-Ethyl-(3-dimethylaminopropyl)carbodiimide (EDC) which gives a urea by-product that is water soluble. It is true that EDC is more costly than DCC but the former is less problematic in the final purification since most esters & amides are water insoluble.