The main point of TF's blue card is for harass and to obtain mana, but with mana regain of only 10 to 50(taking into account the mana cost of the ability), but due to TF's range(525) harassing leaves him very vulnerable to getting harassed as well, and due to how TF is extreamly squishy, using Blue Card isn't the best tool for harassing an enemy laner, unless they are melee, but even then red card provides a better harass and is safer to use in almost all situations, and seeing as 10 mana is almost nothing, and be be obtained but just killing 3 minuions with dorans ring what becomes the point of Blue Card.

Pre-Nerf Blue card asumming TF builds no AD could restore 56 to 142 Mana, and yes this value was a bit high but to nerf the mana gain to 10-50 is a bit much and it can be felt in his game play, in my opinion blue card is rather weak and underwhelming

Edit: I should have put regained mana than gain mana.