Dynamically add rows in ASP.NET MVC table form

Change your

<button id="add" type="submit" class="btn btn-primary">Add</button>

into

<button id="add" class="btn btn-primary">Add</button>

I don't think Add button should do a submit.

Then remove src="~/bundles/jqueryval.js" part from your script tag. According to this answer, we should not leave src attribute here.

Like this

<script type="text/javascript">
    var counter = 1;
    //... the rest of your code is here...
</script>

If you actually have a jqueryval.js file, put it in another <script> tag.

Here is the result you are expecting if I'm not mistaken.

var counter = 1;
        $(function () {
            $('#add').click(function () {
                $('<tr id="tablerow' + counter + '"><td>' +
                    '<input type="text" class="text-box single-line" name="ClientSampleID[' + counter + ']" value="" required="required" />' +
                    '</td>' +
                    '<td>' +
                    '<input type="text" class="text-box single-line" name="AdditionalComments[' + counter + ']" value="" required="required" />' +
                    '</td>' +
                    '<td>' +
                    '<input type="text" class="text-box single-line" name="AcidStables[' + counter + ']" value="" required="required" />' +
                    '</td>' +
                    '<td>' +
                    '<button type="button" class="btn btn-primary" onclick="removeTr(' + counter + ');">Delete</button>' +
                    '</td>' +
                    '</tr>').appendTo('#submissionTable');
                counter++;
                return false;
            });
        });
        function removeTr(index) {
            if (counter > 1) {
                $('#tablerow' + index).remove();
                counter--;
            }
            return false;
        }
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<fieldset>
        <legend>Sample submission</legend>
        <table id="submissionTable" class="table table-bordered">
            <thead>
                <tr>
                    <td>Sample ID</td>
                    <td>Additional Comments</td>
                    <td>Acid-stable amino acids</td>
                </tr>
            </thead>

            <tr id="tablerow0">
                <td>
                    <div class="editor-field">
                        <input class="text-box single-line" name="ClientSampleID[0]" type="text" value="" required="required" />
                    </div>
                </td>
                <td>
                    <div class="editor-field">
                        <input class="text-box single-line" name="AdditionalComments[0]" type="text" value="" required="required" />
                    </div>
                </td>
                <td>
                    <div class="editor-field">
                        <input class="text-box single-line" name="AcidStables[0]" type="text" value="" />
                    </div>
                </td>
                <td>
                    <button type="button" class="btn btn-primary" onclick="removeTr(0);">Delete</button>
                </td>
                <td></td>
            </tr>

        </table>
        <p>
            <button id="add" type="button" class="btn btn-primary">Add</button>
        </p>
        <hr />

        <p>
            <input type="submit" value="Create" class="btn btn-default" />
        </p>
    </fieldset>

Let me know if it helps.