As you can see in the title, it is possible to delete the old transaction in the blockchain?
No, because each and every transaction gets validated over the network by each peer using the clients (be it core or electrum or any that needs to download the whole blockchain). Why would anyone use this technology at any cost and why would Bitcoins be so trustworthy if such vulnerable possibilities would be there? There's nothing that can be done except double-spends.
For more on double-spending:
https://www.bitcoin.com/info/what-is-bitcoin-double-spendingBlockchain is a ledger that is completely locked block-by-block bit-by-bit and can not be touched nor manipulated at any cost.
Double spending, if successful, also doesn't delete older transactions, simply invalidates them. And this only from the point forth on the new valid chain. Anyone wanting to double spend to invalidate a certain tx would have to do it really quickly, or even prepare the attack before the tx... preempting the tx otherwise even a successful attack would still contain the tx made before the point of attack.
By any means, I never told them that double-spending gives anyone the ability to delete or manipulate blockchain. It was just for information purposes only. Though double-spending is a disadvantage, it also cannot be considered a vulnerability to the entire blockchain system. The blocks validated by miners are so secured, because the whole network needs to go block-by-block in order to get each of their future transactions validated in upcoming blocks, so the older blocks have no such probabilities howsoever that they can ever be teased.