I have been waiting to see if a motion to dismiss was going to be allowed, and it appears so. I wrote about this possibility several times above and still think its the best course at this time, even though it is not what Trump seeks and might even hurt him in terms of the upcoming election.
In real life, in civil cases, the way a motion to dismiss works in federal court is to say "even if we assume everything the plaintiff says is true and correct, plaintiff has still not stated a cause of action." These motions are made pre-discovery, that it to say just on the pleadings themselves, considering nothing else. Motions made during or after discovery are most commonly motions for summary judgement (they will include some of the discovery, external to the pleadings - which would, in turn, then involve the application of a different legal standard of review).
There are a few different ways motions to dismiss work - sometimes you cannot make any sense of what the plaintiff wants. Sometimes, there is no legal remedy for what plaintiff seeks (Example, "I want the sun to come out" - I saw that once. And everyone agreed but there was no legal remedy). Probably most often is that there is no statutory, constitutional or other legal support for the cause. You cant ask a court to do something a court lacks the power or jurisdiction to do. This is why the rules allow you the chance to get this resolved before going through the time and cost of discovery.
When granted, motions to dismiss are usually granted "without prejudice." Which means the complaint can be filed again. The court is telling the plaintiff, go back, cure the defects with your complaint, then file again. A motion to dismiss granted "with prejudice" means the same plaintiff cannot file the same case again. While this happens less frequently, it does happen and the grounds are too varying to go into (such as a "vexatious litigant" - someone who has already filed the same nonsense 100 times before).
In this matter, a motion to dismiss is the first thing the Trump side should do. It would be saying "even if everything the House Democrats are saying is true, they still have not stated grounds for removal from office under the Constitution." The Senate would then take the time to explain to the House Democrats what the defects are with their Articles and tell them it is being dismissed "without prejudice," which gives them the opportunity to go back, cure their defects and then refile.
The reason this motion should be made and granted is bigger than Trump. This procedure is going to be setting precedence for all who comes after Trump. And unless we want to see a repeat every single year of what Schiff was doing in his top secret SCIF, then the Senate needs to tell them what was wrong with it.
To me, the largest defects were the ones that made what they did unconstitutional. Manly the denial of due process. The denial of basic American legal rights. Here, Trump could not call his own witnesses. He did not have his own attorneys present. The Committee leader was allowed to instruct witness not to answer questions from the other side. The House Republicans were not allowed to fully cross-examine witnesses. The only people from the opposing side who were allowed to participate where those approved by the Committee leader --others who had a right to participate and who sought to participate, were denied that opportunity. The Committee leader was also allowed to hide the testimony of witnesses from subsequent public witnesses, the full House and even their bosses (the people) -- this should never happen and alone is enough to make the whole thing defective. The president was never allowed to confront his accuser, was not allowed to depose him and indeed was never even allowed to know his identity (a direct violation of the 6th Amendment). All this is just off the top of my head, there are other grounds.
And so it is important to set some rules for this. Make it public. Say it on live TV, under oath, and then put it in writing, in simple terms for everyone to see. So, yes, the Senate should say these Articles are too legally defective for it to consider at this time and here is why. They should take the time to explain that the procedure of the House Desm was defective, that what they did was not legally sufficient under the American system of justice. They should also say they are dismissing the Articles "without prejudice" and will reconsider the case if the House goes back and cures it. And then actually tell them, "here is what you need to do to fix it." IMO, it's very important that the Senate make clear the process itself must be fair to everyone. Even Trump, and for all presidents after him.
Procedurally in the Senate, the way I would go would be that once the Senate is called to order, the House Dems state their case, but then before anything else goes forward, before the House Rs or the President responds, before any witnesses, the motion to dismiss is made.