If you do not like a gift that you bought or received, you can exchange it for a more expensive gift. Tap the current gift (the 'glass' icon is usually located in the same place), then buy the new gift. It will then be displayed next to your avatar. You can also exchange another player's gift. Gifts disappear after a certain time. It is worth remembering that VIP gifts for gold last longer than ordinary gifts.
You can disable the display of gifts at the game table if they distract you from playing. To do this, use the corresponding switch in the settings menu. Note that you will not be able to give or receive gifts if you do this.