With 20 sat/byte, and an unconfirmed parent with the same low fee, I expect the transaction to be dropped from mempool eventually.
Anyway this is unconfirmed, and we don't want to find ourselves again sending Bitcoin funds using our wallet and getting them stuck because of this potential "Parent" transaction
I'm not sure how blockchain.info handles this, but I assume you can opt not to use unconfirmed inputs in your own transactions.
If anyone wants those 0.001 BTC for free by all means come and take them, just let us know how to get rid of this transaction and remove it from our wallet please.
You'll need to hand over your private key to someone in order to "take it". That would give that person access to the remaining 0.00353186 BTC in your wallet too, so don't do this.
If blockchain.info allows you to select the unconfirmed input for a transaction, you can send 0.00002
BTC to 1BitcoinEaterAddressDontSendf59kuE and use the remaining 0.000101632
BTC as fee. This way, it doesn't matter if it triggers CPFP and confirms, or the original transaction gets dropped from mempool. One way or another, it'll be gone for you.