I commend you for honoring your parents by sending them to perform Umrah. I pray to Allah to reward you in both worlds. I also pray that Allah blesses your parents in realizing their cherished dream and return home safely.
As for your question about taking a loan for this purpose, there is nothing wrong with it as long as you can afford to pay it back on time.
In conclusion, you are allowed to take a loan to pay for your parent's Umrah if you are solvent.