If the Samsung phone was an unlocked version then inserting the t mobile sim card would have only added certain features which would then disappear when removed from the phone.
The tmobile sim card certainly wouldn't introduce a start up splash screen.
I'm guessing the store you bought it from sold you a branded Samsung phone that was intended to be used on tmobile and gas been since unlocked to all networks.
If you download the phoneinfo app from the Playstore and then see what the active CsC is you'll be able to check the phones status.
Does the phone accept other network sim cards ?
You can use package disablers from the Playstore to remove certain unwanted apps but be careful on what you remove.
This wouldn't however remove the tmobile start up splash screen.
Only putting on a Custom Rom would probably do that but again you need to be very careful and be aware of the pros and cons of doing this.
Disclaimer 》 Adding a Custom Rom can cause stability issues and in the extreme cause a phone not to work. Thus a person carries this procedure out at their own informed choice.
A Samsung phone typically has a 2 year warranty on them but if a person has imported a phone from one country to be used in another then they wouod have to check the warranty T&C's and small print to ensure they can get support from the Samsung Support Department they are now in.
A Samsung Experience Store / Samsung Service Centre would also be able to confirm wether they can offer support or not.
Daily Driver > Samsung Galaxy s²² Ultra 256Gb in Phantom Black.
The advice I offer is my own and does not represent Samsung’s position.
I'm here to help. " This is the way. "