You can deduct the payment as a charitable contribution if you have one of the following. The wording is from IRS Publication 526.
"A receipt (or a letter or other written communication such as an email) from the [shelter] showing the name of the organization, the date of the contribution, and the amount of the contribution."
"A bank record that shows the name of the qualified organization, the date of the contribution, and the amount of the contribution. Bank records may include a canceled check, a bank or credit union statement, a credit card statement, an electronic fund transfer receipt, or a scanned image of both sides of a canceled check obtained from a bank or credit union website."
If the payment was $250 or more, there are additional requirements for the acknowledgement from the organization. The IRS is strict about the substantiation requirements for charitable contributions.
For 2022, charitable contributions are an itemized deduction. The deduction will not reduce your tax or increase your refund unless your total itemized deductions are more than your standard deduction.
(For 2020 and 2021 you could deduct a small amount of charitable contributions directly from your income, even if you did not use itemized deductions. As of now that option has been eliminated for 2022 and later.)