Can one use a water jug with ice on shabbos, if when you pour the water there is a wide filter/catcher to stop the ice from coming out? Or perhaps it is an issue of borer/merakeid?
CLYOR. To me it seems permissible, unless you hate ice, and plan on emptying the pitcher.
It is definitely not borer for several reasons:
- It involves taking the good from the bad, so even if you hate ice, you're ok (see 39 Melachot p 404).
- It's not even a mixture according to Rabbi Ribiat, quoting Rav Moshe (ibid 391 and footnote there)
- Zoreh, Borer and Meraked are so similar that it can be hard to separate them in halacha. This shayla would fall under meraked and not borer as you aren't doing it with hand or similar; you are straining it - see ibid 382 (and you aren't using any form of wind/air power so it's not zoreh either - ibid 379 and footnotes there).
For meraked, the pesolet has to be undesireable. Generally, it means undesirable to most people (ibid 511, quoting Mishna Berura 319:34), which does not include ice. The exception would be if you are particularly averse to ice (ibid 514, quoting Pri Megadim 319, Mishb'tzot Zahav s'k 6, and Biur Halacha there, 10), then you will still be ok if you don't pour it out completely, but leave some behind (based on S'A O'C 319:14).
After considerable Google search I found this Menucha youth Parasha sheet: https://btya.org/wp-content/uploads/MenuchaV02I28.pdf
Using a Pitcher with a Slotted Cover
-- by Shlomo Epshteyn
The spring is finally here. For the first time since last summer, the Mermelstein family put on a Shabbos table a pitcher of water that had ice cubes in it. Everyone noticed the brand new pitcher that the father purchased on erev Shabbos. Shmuli noticed, however, that the cover of the pitcher had a "filter" to hold back the ice. "Abba – but you taught me that we can‘t use a kli to do Borer even if we are selecting 'good' from 'bad' for immediate usage."
Question: Can this pitcher be used?
Answer: Yes. However, once the ice cubes have become small (i.e. to a degree where it is no longer very easy to remove them), it is better to pour the water when the ice cubes are settled at the bottom of the pitcher. If the ice cubes are small and the water level is very low, where it does not rise above the ice cubes, it‘s best then to add more water to the pitcher.
Explanation: We have learned in the last few articles that the melacha of Borer is not applicable in a case where a large item is inside a liquid, whereby it does not require effort to identify and remove the item from the liquid. There, the item is already considered as 'selected' - i.e., it is lacking the status of "mixed-in" .
An example of such is a case where the eggs are inside the water. Spilling out the water or removing the eggs from the water—even for later use—is permitted. Since the eggs are large and don‘t require effort to identify and remove them, they are not considered as "mixed in" with the water .
Similarly, the Shemiras Shabbos Kehilchosa rules that due to their considerably large size, ice cubes inside a drink* are not considered as mixed in with the liquid . Since there is no "mixture", then even a kli (i.e., the cover which holds back the ice) may be used in this case . (The second part of the "Answer" – what to do once the ice cubes in the pitcher become small – is similar to a case of "a tea pot with essence and tea leaves." The explanation of these cases needs to be discussed in a separate article.)
 Shevisas HaShabbos (Borer, 25).  ibid.  Shemiras Shabbos Kehilchosa 3:63.
* From the fact that the Shemiras Shabbos Kehilchosa (3:4) taught that one may remove a large piece of meat from a clear soup (since it does not take effort to identify the meat there), it appears that in a case of ice cubes, the “drink” that Shemiras Shabbos Kehilchosa is referring to is also a type of drink in which one could see the ice cubes (e.g., water, apple juice).