IIRC, it's not the brush, but the form of the Easy-Off, as the aerosol version contains either alcohol, or some derivative of it that is not permitted under certain authorities.
There are certain stringencies that are followed during the Passover holiday period regarding many popular cleaning products that do not need to be adhered to during the rest of the year.
The goopy form of Easy-Off that comes in the container with the brush is brushed on rather than sprayed, and then allowed to sit.
There is a newer product named "All Gone" by St. Moritz that is popular in the Orthodox community that is permitted, but it is the most toxic, noxious cleaning chemical that many moms refuse to allow in their houses, as the fumes have seriously sickened children (another such popular chemical that is similarly dangerous is a floor finish called "Moisture Cure", extremely resilient on the wood flooring used in Brooklyn in lieu of the carpeting that the Orthodox shun).
It is permitted to place a boiling hot pan of water in the over beforehand to soften whatever crud lurks within, but I was always directed not to add ammonia to the water.
The broiler pan and racks are not considered to be clean unless you run a blowtorch over them (yes, this is true). After this, every inch of the oven's interior, racks and all, must be lined with aluminum, and it is then declared off-limits until the onset of the holiday.
A lot of the cleaning procedures are steeped in ritual and seem old-fashioned, by today's standards (for instance, you clean a stainless steel sink and then kasher it by pouring a specific, predetermined amount of boiling water in it, over the sides and on top), and appliances that have been kashered for Pesach are marked as such and not used.
Most of the cleaning products commonly used for Passover cleaning tend to be the old-school ones and I always assumed (correct me if I'm wrong) that, since the oven cleaner with the brush had such a dated look to it, it was actually a throwback to the postwar era.
Also, none of what I've written here should be interpreted as halachically accepted, universally accepted gospel regarding Passover cleaning procedures...rather, it is simply what I observed and participated in, at a time in my life when I had exposure to a particular, religious community.
For official instructions, please consult your local Orthodox rabbi...
