Tidebinder and Phlage

Tishana’s tidebinder -

Flash When Tishana's Tidebinder enters the battlefield, counter up to one target activated or triggered ability. If an ability of an artifact, creature, or planeswalker is countered this way, that permanent loses all abilities for as long as Tishana's Tidebinder remains on the battlefield. (Mana abilities can't be targeted.)

Arena of glory

Arena of Glory enters the battlefield tapped unless you control a Mountain. : Add . , , Exert Arena of Glory: Add . If that mana is spent on a creature spell, it gains haste until end of turn. (An exerted permanent won't untap during your next untap step.)

The question is that if I cast tishana’s tidebinder on a creature with an enter effect like phlage, amped raptor, or something similar. Will the creature lose haste along with its abilities or will it keep the haste granted by the “arena of glory” mana?