How much does carbaryl and carbofuran interfere with melatonin?

Good question I think in the paper they used a few measurements the simplest one being that in the docking simulations they bound about 20-30% less than melatonin itself which is quite a strong effect. How this applies in a living subject is hard to say though and would need further research.

And would washing fruits and vegetables with carbaryl and carbofuran remove wash it away?

It certainly helps to reduce exposure - some small amounts might still remain. There is a paper which discusses it here:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3907644/

Here is an excerpt:

"In case of carbaryl the initial deposit as a result of two application dosages reduced to 5.94 and 12.24 ppm respectively by tap water washing of okra for 30 s. Thus, washing decreased the carbaryl deposit by 66.12 and 69.55% for lower and higher application dosage, respectively. Various pesticide decontamination processes like washing the fruits with water were reported to dislodge the residues to varying degrees depending on constitution of the fruit, chemical nature of the pesticide and environmental conditions. Washing was the most effective means of removing pesticide residues and minimizing dietary intakes from cabbage (Yuan et al.2009). Elkins et al. (1968) also reported that cold water washing removed 96% malathion residue from beans."