Considering that the main clause (I'll have a word with Tom) is the condition and the subordinate clause contains the consequence (If it will ease your mind), the action expressed in the main clause takes place before the subordinate clause, that's why the subordinate clause in the future tense.
If it will save our marriage, we'll have a baby.
Unlike traditional IF clause in which the condition is in the subordinate clause (which always takes the present tense) and the consequence is in the main clause (generally Will-future)
If he calls me I will give him your message.
First he has to call me, then I'll be able to give him your message.
Not all if-clauses are conditional clauses. The sentence, If it will ease your mind, I'll have a word with Tom, is not a conditional sentence, actually. Here, if means if that is the case or if it's true that.
Well, I cannot find any condition in the above sentence.
Surely the condition is whether it will ease A's mind or not.
If it will, B will have a word with Tom.
If it won't, B will not have a word with Tom.
It's now up to A to respond "Yes, thank you, it will" or "No, don't bother. Tom can't help"
Point well taken and very many thanks for your time, but I wonder if the second sentence is really incorrect. Can we use two sentenses in two different situations?
Yes, but only if you have correct context surrounding it. What does it stand for in the following?: -If it eases your mind, I'll have a word with Tom. If it stands for my having a word with Tom, it requires the future tense.
If it stands for something else, it might be possible as in the following: A: I have an uneasy mind.
B: Take this valium tablet. If it eases your mind, I'll have a word with Tom - he has loads of this stuff. But that's very contrived.