Yep, just as I thought, it's not an <a> element, it's just plain text. So it's not a link, you are seeing your email program try to create a link from the text and the email program doesn't know where it ends, so it ends it at the first space it finds.
You need to have it set-up as an actual link in your email. Not only will this solve your problem with the spaces, but it'll also look cleaner, because we can do a different label on the link than the actual URL (I've done "Open the Form" in the example below).
Here's the exact text you posted, but with the URL modified to function as a link (an <a> element) instead of text. You should be able to just copy/paste this right into the HTML view of the Email Service Task within forms.
</p><p class="MsoNormal"><span style="font-size: 10.5pt; font-family: "Open Sans", sans-serif; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">Please click the following link to review this request: </span><o:p></o:p><span style="font-size: 14px;"><a href="https://lfweb.tompkins-co.org/Forms/my2GR?Payee_First_Name_={/dataset/Payee_First_Name_}&Payee_Last_Name_={/dataset/Payee_Last_Name_}&Check_Date_={/dataset/Check_Date_}&Check_Number_={/dataset/Check_Number_}&Check_Amount_={/dataset/Check_Amount_}&Reason_for_Stop_Payment_={/dataset/Reason_for_Stop_Payment__1}" target="_blank">Open the Form</a></span></p><p class="MsoNormal"><o:p></o:p></p><br><p class="MsoNormal"><br></p><p class="MsoNormal"><br></p><p class="MsoNormal"><br></p>
Tip - When you are writing a post, use the "code" button (shows {....} and the word code) in the post editor to do code posts like that, which are usually easier to read on the screen. Then when you are reading a post, use the "view source" button (looks like a paper with < and > sumbols on them) to see the code in a format that is easier to copy from.