Arbitrage:
Any commodity of sufficient value in their world to justify the expenditure of magic in their world rapidly disappears.
What items have value there depends on a lot of factors.
What's the cost of summoning an item? presumably low if it can be used for summoning water for irrigation.
If the manna needed to summon one gold bar costs less than a gold bar then Fort Knox will empty until the price of manna rises or the price of gold falls in their world.
Data exchange:
The other world can far more easily gather data about us by summoning books of all kinds. This would also give them detailed info on commodities and goods available in our world and approximately where.
If geography matches then the locations of ore reserves are also likely to match. Any canny mage in their world is likely to summon mining surveys which will let them know where the unexploited reserves are in their world.
If this society is using our world as a rubbish dump then we're likely to be able to gather a great deal of info from their garbage and discarded paperwork. Of course if anyone writes this down in some book or paper that gets summoned away the other world might know to start shredding/burning their garbage before sending.
War and blackmail:
If the cost of manna is low enough then they could hold us hostage by threatening to summon away all the oxygen from an area or threatening to dump magical weapons into an area. They might start demanding tithes and specific goods be prepared in such a manner as to make summoning them cheaper.
Trade and smuggling:
There's also the possibility of less violent trade. If the cost of Manna is high and if there's anything we can do on our end to make the summoning of items cheaper then mages could trade with drug lords, they lay out guns and wrist watches in a perfectly aligned summoning grid, the mages in exchange summon heroin from pakistan and banish it into a basement in new-york.
You get very different answers depending on the cost of manna and depending on whether people in our world can do anything to assist with the process to reduce the manna-cost or if custom goods are of great value on the magical side.