That's a good question. Generally, an owner or contractor can't unilaterally release someone else's mechanics lien without some sort of official action - like with the Notice of Contest filing mentioned in that previous answer, or by challenging the filed lien in court. So, an owner stating that they'll simply removing the filed lien in just a few days might just be them bluffing.
However, an owner or contractor could have the lien discharged by bonding off the filed lien. If that's done, the claim wouldn't simply disappear, though. Rather, when a lien is bonded off, that lien is transferred off of the property title and onto the bond. In that case, the lien claimant might have to file suit against the bond in order to recover payment - but, that's not all that different than having to file suit to enforce the lien. At the end of the day, though, having a mechanics lien bonded off isn't all that bad. Levelset discusses that here: Don’t Be Afraid Of Threats To Bond Off Your Mechanics Lien: Explaining Mechanics Lien Bonds.
But, as mentioned above: other than having a lien bonded off, the process of having a lien removed from the property is hardly instantaneous, and the lien claimant will very typically have the opportunity to dispute any claims that their lien is improper.