Ya ride in on a "Skate Board", ya get tossed out the door.
To be more accurate, if you ride in on a skate board you will be asked to leave. The sign didn't legally prevent you from coming in, and it won't legally make you leave because it has no weight of law. HOWEVER, once you are asked to leave, you are now trespassing and you are obligated to leave. It's the request to leave that creates the obligation to leave, not the sign itself.
It's actually pretty similar in one small way to the situation under discussion.
...violating that sign can get you removed from the premises.
No, it can not. A non-compliant sign has no weight of law and a TX handgun license holder has no obligation to avoid premises or leave premises so posted. A licensee can NOT legally be removed from the premises purely on the basis of a non-compliant sign.
In the case where a non-compliant sign is posted, the owner, or the owner's agent would have to verbally notify the licensee to leave in order to create any obligation on the part of the licensee.
Being removed for disobeying a sign, is a ban.
Well, first of all, a licensee will not be removed for solely for disregarding a non-compliant sign. They would have to be verbally notified which is a compliant means of removing/barring a licensee from carrying on the premises.
Second, it's not quite accurate to imply that ignoring a non-compliant sign constitutes disobedience. It would be just as accurate to say that a person who loves Jesus is "disobeying" a bumper sticker that instructs him or her to honk if he loves Jesus. A non-compliant sign has just as much legal weight as the bumper sticker.
The obligation to leave (or avoid) the premises only comes if the licensee is notified by one of the means defined in TX law.
So IF you ever move to TX, and IF you ever own a business here, and IF you ever wish to ban handguns in that business, you will have a lot more luck in your endeavor if you read the 30.06 & 30.07 sections of the TX Penal Code and follow the prescribed methodology for doing so.
You will find that posting typical "No Guns" signs will have no effect as the TX handgun license class teaches (and TX law makes it clear) that they are not an effective means of notifying handgun license holders not to carry on the premises.