You cannot claim a grant that was not awarded to you. Even if your name was on the grant, there will be stipulations written in that says what happens if someone on the project leaves the university. As an undergraduate, you would not be able to take any part of the grant with you to another university, so walking away from your current school means you walk away from the grant. The only way this grant will benefit you is if you stay and work on the project and are listed as a co-author on a future paper once the work has been completed.
You need to speak with faculty members who are familiar with how the research world works before claiming credit for things like this. You can absolutely ruin your chances to get into other programs in the future if you make a misstep like this–not to mention, you need good references from faculty familiar with your abilities in the lab and it sounds like what you are doing now could burn some bridges with your current mentor.
Final word of advice: it is extremely difficult to get the kind of research experience that you are describing as an undergraduate. It typically only happens at less competitive schools that cannot fund postdocs and have limited graduate students to rely on. You are much better off staying put and continuing to gain research experience at your current school and leveraging that to go on to grad school elsewhere. Lab and research experience goes a long way for grad admissions and postdoc offers, and selective schools with top grad programs rarely offer undergrad research experience like you are describing.