In a 1031 exchange the money would not come from the seller but from an intermediary that's holding the proceeds of the property they sold, as such there might be mention of the 1031 exchange in the contract noting the name of the intermediary or just that an intermediary will be used. I don't know if this is required/customary in your region.
A company in my state that acts as an intermediary (First American Exchange Company) says:
In addition, the taxpayer must provide written notice of that
assignment to all parties to the contract, and it is usually advisable
to get the other parties to acknowledge they have received the notice.
The assignment and notice are required in connection with both the
sale of the relinquished property and the purchase of the replacement
It doesn't have impact on the selling process, but perhaps some sellers don't want to sell to landlords and agents have found its best to ask up front, rather than having offer declined when they see the 1031 language in the contract.
There is a timing component to 1031 exchanges but it is likely not the reason they mention it. They have a window of time between selling and identifying/closing on the replacement property, but it exceeds standard closing timelines.
If the buyer is running out of time to identify potential properties it would give you some extra leverage.